Exponential function questions and answers pdf. These often occur in models of real-life situations.

Exponential function questions and answers pdf Dec 17, 2024 · When solving application problems that involve exponential and logarithmic functions, we need to pay close attention to the position of the variable in the equation to determine the proper way solve the equation we investigate solving equations that contain exponents. They sketch the graphs of single transformations and multiple transformations and identify any effects that the transformations have on the domain, range, and asymptotes of the functions. Dont spend too long on one question. 5x3 + ax2 + b completely, and hence solve the equation 53y+1 + a × 52y + b = 0, giving any answers correct to 3 significant figures. AT- ike Math Questions Topic: Mathematical Models Calculator NOT Pe Easy: 1. The last two properties are useful for graphing and writing exponential functions. f ( x x 1 ) 3(4 ) Worksheet # 3: The Exponential Function and the Logarithm (a) Graph the functions f(x) = 2x and g(x) = 2 x and give the domains and range of each function. The document contains a worksheet with exponential functions word problems and their answers. Find the inverse of each function in Exploration 1. On the diagram in your answer booklet, sketch the graph of the inverse function. 9E: Exercises on Derivatives of Logarithms and Exponential Functions is shared under a CC BY-NC-SA 4. Use the graphs and tables of 6. com They used functions to model relationships between quantities and also worked with exponential notation and applying the properties of integer exponents to solve equations. Increasing Linear B. Therefore the expo 3x + 2 = 2x + 2 2) Given the following exponential equations, state whether they are increasing or decreasing. 0 Introduction This chapter will introduce you to the hyperbolic functions which you may have noticed on your calculator with the abbreviation hyp. Passes through 0, 3 , 1, 5 , 1, 7 3 Horizontal asymptote: y 2 Therefore, it matches graph (b). characteristics of the same graphs. com You must know ALL the rules for finding derivatives. Question: Why do we limit the base to positive values? Answer:To ensure that the outputs will be real numbers. Decide whether the expression has been simplified correctly. Draw the graph of each of the following logarithmic functions, and analyze each of them completely. 1{3. If you are a teacher, please note that the sheets have been designed so that they may be laminated back-to-back (questions on one side and answers on the other) and used in a classroom setting. f (x) = log 4 x The inverse function, f 1 exists. A: Concepts Exercise \ (\PageIndex {1}\) 1) How can an exponential equation be solved? 2) When does an extraneous solution occur? How can an extraneous solution be recognized? 3) When can the one-to-one property of logarithms be used to solve an equation? When can it not be used? Answer 1 Determine first if the equation can be rewritten so that each side uses the same base. The diagram below shows the graph of the function f (x) =log4 x, where x > 0. Therefore the equation can be written 6 (6 1) 3x 2 = (62)x+1 Using the power of a power property of exponential functions, we can multiply the exponents: 63x+2 = 62x+2 s one-to-one. 025)^x ; $10. Does this function represent exponential growth or exponential decay? 3. This page also shares a short review of the laws of exponents in case you need some help solving the problems on our free exponents worksheets. This inverse function is called a logarithmic function with base b. 4. Identify the choice that best completes the statement or answers the question. It then follows that the anti derivative of ex is ex: Free lessons, worksheets, and video tutorials for students and teachers. Given a formula for an exponential function, is it possible to determine whether the function grows or decays exponentially just by looking at the formula? Explain. As the independent variable x changes by a constant amount, the ≠ dependent variable y is multiplied by a constant factor, which means consecutive 2. Create your own worksheets like this one with Infinite Calculus. An exponential parent function is y = 2x. Do all exponential functions have a horizontal asymptote, and how do you know what it is when you look at the equation? giving the answer in the form k k+ln , where kis an integer. When working with exponential functions, re-member to use the various rules of exponentia-tion. Determine if each function is increasing or decreasing. com This document contains an exponential and logarithm quiz with 10 multiple choice questions and their answers. Derivatives of Exponential and Logarithmic Functions MULTIPLE CHOICE. 0 license and was authored, remixed, and/or curated by OpenStax. Students apply the general transformation function g (x) 5 Af(B(x 2 C)) 1 D to exponential and logarithmic functions. Exponential and Logarithms IB Exam Practice Questions ne tial and Logarithms – IB Exa University of Sydney 1 Derivatives of exponential and logarithmic func-tions If you are not familiar with exponential and logarithmic functions you may wish to consult the booklet Exponents and Logarithms which is available from the Mathematics Learning Centre. Answer. Write an exponential function to model this situation, then find the price of a ticket in 2025. TEKS 9B Write an equation for the function that includes the points (2, 100) and (3, 1000) Here is the list of Logarithms MCQ questions and answers available online and pdf download format to practice for exams. 7: Graphing Exponential Functions 1 The graph of y ax , where a 0, contains the point (1,0) Nov 16, 2022 · Here is a set of practice problems to accompany the Solving Exponential Equations section of the Exponential and Logarithm Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. 3) Write an exponential function to model each situation. The graphs of two The graph of functions are shown on the right. Name. 1: Derivatives of Polynomials and Exponential Functions 1. Topics in this unit include: exponential growth, exponential decay, compound interest, graphing exponential functions, and transformations of exponential functions. m. F. The bank of exam style questions are accompanied by high quality step-by-step markschemes and video tutorials, taught by experienced IB Mathematics teachers. 2 Change in Linear and Exponential Functions Write your questions and thoughts here! Evaluating Exponential Functions Worksheets These Algebra 1 - Exponents Worksheets produces problems for evaluating Exponential Functions. 4 The number bigger can isn’t be even the base of a base, and an big plenty number of numbers to be using are much, for a base (any positive exponential function, the faster much its bigger graph than grows as it moves to the right. 4 CRITICAL THINKING Is the graph of a set of points enough to determine whether the points represent a linear function or an exponential function? Justify your answer. Decreasing Linear row Chapter 5: Exponential and Logarithmic Functions 5-1 Exponential Functions Exponential Functions: - a function where the input (x) is the exponent of a numerical base, a. Differentiation - Natural Logs and Exponentials Differentiate each function with respect to x. Logarithmic Di erentiation Derivative of exponential functions. Give the domain and range of the inverse function. 5), what is the equation of this function? The change of base rule: log a c = log c b There are two common abbreviations for logarithms to particular bases: log 10 x is often written as log x loge x is often written as ln x The graphs of exponential and logarithmic functions: y = Aex = C + Ae−x C) f(x) = 8. The inverse of the relation is 514, 22, 13, -12, 10, -226 and is shown in red. 5. ECE 313 Course Notes, Sections 3. ) The function below is best described as which of the following? A. (1 mark) Estimate a possible value of “b” if the general form of an exponential function is a(b)x ? (1 mark) The probability density function of the exponential distribution is de ned as f(x) = e x for x 0 and f(x) = 0 for x < 0. 9 Connecting a Function, Its First Derivative, and Its Second Derivative 6. 4 The Fundamental Theorem of Calculus and Accumulation Functions 6. Exponential functions play an important role in mathematical analysis. The natural exponential function can be considered as \the easiest function in Calculus courses" since the derivative of ex is ex: General Exponential Function ax. 15. Try With your table complete the following matching 6. It is very important in solving problems related to growth and decay. 02) t , where t represents the number of years since the current population count. #2: Sketch the function y = 3 (2) x 1 on the grid provided and state the domain, range, the equation of any asymptotes, and the value of any intercepts. (a) Solve 102x+1 = 100. It is symmetric with respect to the x-axis. IF. For those that are not, explain why they are not exponential functions. Choose the best answer. The Oxford Dictionary defines the word nominal as a value that Find the population one hour from now, two hours from now, etc. Answers to Review Sheet: Exponential and Logorithmic Functions (ID: 1) 1) 6log u − 3log v 2) 4log u + 4log v 6 6 log 8 log 7 log 11 The IB Math Analysis and Approaches (AA) SL Questionbank is a comprehensive set of IB Mathematics exam style questions, categorised into syllabus topic and concept, and sorted by difficulty of question. (c) Graph the inverse function to f. Questions and model answers on Logarithmic & Exponential Functions for the Cambridge (CIE) IGCSE Additional Maths syllabus, written by the Further Maths experts at Save My Exams. To mention a few examples: Under ideal conditions the number of bacteria present at any time t in a culture may be described by an exponential function of t; radioactive Create your own worksheets like this one with Infinite Algebra 1. Topics include logarithm laws, graphing, exponential equations, growth and decay models, 1⁄2 life, and more = log ( x − 5) 5 = log 5 x2 = log −2 x3 4 = log ( x4 5 + 7) = log ( −3 x4 3 + 8) = log ( −2 x2 + 4) 3 = log ( x + 8) 5 = log −4 x 1 4 = log ( x5 4 + 1) = log ( x2 + 2) 5 y = log ( 2 ⋅ 5 3 − 9) MadAsMaths :: Mathematics Resources Exponential Growth and Decay Recall from Section 1 that exponential functions are sometimes known as growth or decay functions. t t2 − t1 is constant. 2). 5% each year. Estimate the x-value at y = 4. Then, use the model to answer the questions. Exam Style Questions Exponential Graphs Corbettmotths Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. This follows chapter 3 of the grade 11 Functions McGraw Hill textbook and chapter 4 of the grade 11 Functions Nelson textbook. Feb 12, 2018 · Exponential Growth and Decay Worksheet 1. These Exponents Worksheets are a good resource for students in the 5th Grade through the 8th Grade. 2. The growth and decay may be that of a plant or a population, a crystalline structure or money in the bank. Graph the first function, Y1, in bold or a different color. [5] 5 A curve has equation 3 ln x + 6xy + y2 = 16. The population of a small town can be modelled by the exponential function P(t) = 5000(1. ECE 313: Problem Set 7: Problems and Solutions CDF and pdf; Uniform and Exponential random variables Due: Reading: Wednesday, March 6 at 6 p. 2 a. Suppose we have an equation in the form: value = coefficient (base) exponent increased by approximately 2. It is asymptotic to the x-axis. Unit 4: Exponential Functions After completion of this unit, you will be able to Learning Target #1: Graphs and Transformations of Exponential Functions Evaluate an exponential function Graph an exponential function using a xy chart Identify whether a function is exponential, quadratic, or linear from a graph, equation, or table 4. For each transformation below, state the base (parent) function and then describe the transformations in the order in which they should be applied. Given y = 1. Here, the rules to use are ea+b = eaeb and ea b = ea=eb. 7: Graphing Exponential Functions 2 If the function g(x) = abx represents exponential growth, which statement about g(x) is false? a > 0 and b > 1 Graph an exponential function using a xy chart Identify whether a function is exponential, quadratic, or linear from a graph, equation, or table Transform an exponential function by translating, stretching/shrinking, and reflecting Identfiy transformations from a function Learning Target #2: Characteristics of Exponential Functions I. 1 Exponential Growth and Decay Functions domain, range, and yintercept. Questions and model answers on Exponentials & Logs for the DP IB Analysis & Approaches (AA): HL syllabus, written by the Maths experts at Save My Exams. Apr 30, 2022 · Example 4 2 e A 1) What role does the horizontal asymptote of an exponential function play in telling us about the end behavior of the graph? 2) What is the advantage of knowing how to recognize transformations of the graph of a parent function algebraically? 3) Explore and discuss the graphs of F (x) = (b) x and G (x) = (1 b) x. Because of their special characteristics, they are some of the most useful functions and are found in virtually every field where mathematics is applied. Apr 22, 2024 · This page titled 3. 01 each year, write and exponential function to model the situation, then find the value of the care in 2020. Use your graphing calculator to graph the four functions shown in each box on the same screen. Extend your table until you can answer the questions asked in Question 6. Practice Assessment 9 Derivatives of Exponential and Logarithmic Functions These practice problems are designed to help you prepare for our course exams and assess your understanding of the course material at the expected level. You will see some connections with trigonometric functions and will be able to find various integrals which cannot be found without the help of hyperbolic functions. The general form of an exponential function with an asymptote of y = 0 is y = abx . Jun 6, 2018 · Chapter 6 : Exponential and Logarithm Functions Here are a set of practice problems for the Exponential and Logarithm Functions chapter of the Algebra notes. 6. 4(0. A. 23x , identify the growth/decay factor, growth/decay rate, and the initial value. Choose the one alternative that best completes the statement or answers the question. Guidance Read each question carefully before you begin answering it. . The IB Mathematics AA SL Question Essential Question What are some of the characteristics of the graph of a logarithmic function? Every exponential function of the form f (x) bx, where b is a positive real number = other than 1, has an inverse function that you can denote by g(x) = logb x. and graph your points. The Exponential Function MCQ App Download: Free College Math App to learn odd functions, composition of functions, hyperbolic functions test prep for best GRE prep courses online. You may select the problems to contain only positive, negative or a mixture of different exponents. = Do you think the statement below is true for any exponential function? Justify your answer. Find the inverse and graph it in red. 81)x f( Answer all the questions showing all your work. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. This table of values represents an exponential function. com = 8 = 8 5) Write the equation for the function that results from each transformation applied to the base function = 7 a) reflect in the x-‐axis (vertical reflection) c) stretch horizontally by a factor of 2. (11) x 125 Looking for free exponents worksheets? This page shares a free library of printable PDF exponents worksheets. If so, the 11. Does this function represent exponential growth or exponential decay? 4. All exponential functions are of the form: f ( x ) z = ± 2 + k 15. ZJJ Z JJ JL ,E to simplify and solve problems using scientific notat Evaluate exponential functions for a given domain. Homework Helper! Units of Study: Unit 1 – Functions Unit 2 – Transformations of Functions Unit 3 – Exponential Functions Unit 4 – Trigonometry Unit 5 – Trigonometric Functions Unit 6 – Sequences and Series Unit 7 – Financial Worksheet 4. 5x – 6, answer questions 5 to 7. Simplify each of the following expressions so that there is at most one exponential expression is in the answer, with an exponent of x. 8 Sketching Graphs of Functions and Their Derivatives 5. II. is a = transformation ) of such that 0 Correct to the nearest tenth, the value of (first two digits of your answer), and the value of can be written as can be written as (last two digits of your answer). Read each question carefully before you begin answering it. 10 that the derivative of ex is ex. It introduces concepts of logarithms including common (base 10) logarithms, properties such as loga(mn)=logam+logan, and types of logarithms. MULTIPLE CHOICE PROBLEMS Indicate (by circling) directly in the table below your solution to the multiple choice problems. Find course outlines, unit outlines, handouts, lessons and homework. 5 What is the equation of the horizontal asymptote? 6 EXPONENTIAL FUNCTIONS WORD PROBLEMS WORKSHEET (WITH ANSWERS) 1. necessary. **Check for extraneous solutions before moving on from each problem. ” Graphing Exponential Functions Work with a partner. 60. Then check your answer by using a graphing calculator to graph each function and its inverse in the same viewing window. (x and y are variables and e is a constant) Question 2 : Find the derivative e mx with respect to x, where m is a constant. Derivatives of Exponential and Logarithmic Functions Derivative of exponential functions. A. Attempt every question. Examples of transformations of the graph of f (x) 4x are shown below. Class 12 Maths MCQ – Exponential and Logarithmic Functions This set of Class 12 Maths Chapter 5 Multiple Choice Questions & Answers (MCQs) focuses on “Exponential and Logarithmic Functions”. III. Download these Free Exponential Functions MCQ Quiz Pdf and prepare for your upcoming exams Like Banking, SSC, Railway, UPSC, State PSC. You may choose up to 1 answers for each multiple choice problem . The first systematic consideration of hyperbolic functions was done by the Swiss Welcome to Grade 11 Functions! Use this page to find all resources worked on in class. com The student is expected to determine the domain and range of exponential A. Ex. 3. – Evaluating Exponential Functions The base of an exponential function must be a positive real number other than 1. For a problem with precisely one answer marked and the answer is correct, 3 points. Use di erentiation rules from Section 3. I have invested a great deal of time in putting this material together. Ask for help, read your notes and your textbook, use your mind. 5t . LE. Designed for Grade 12 students, this resource includes multiple practice problems with detailed explanations and graphs. The parameters a, b, c, and d, which represent real numbers can be used to transform the absolute value parent function: y = a2x, y = 2bx, y = 2x – c, and y = 2x + d. without a calculator. f(x) = 4. The natural exponential function can be considered as \the easiest function in Calculus courses" since the derivative of ex is ex: Exponential and Logarithmic Functions Recall from worksheet 3. Question 3 : Find the derivative e -x with respect to x. Free trial available at KutaSoftware. Assessments Advanced Functions: Chapter 7: Practice Problems - Exponential and Logarithmic Functions Here are some practice problems! Some of these are easy, some aren’t. Here is a worksheet with list of example exponential limits questions for your practice and also Click a link below to access the Algebra 1 worksheet for a specific section. NR #6 The values of , , , and Example One Determine the base function of following exponential functions and then determine the transformations of each base function. 10 Derivatives of Log Functions & LOG DI ho ns (a)(a) y = xa (b) y = a x (c) y = x x (d) y = a a 2. Give an exact solution. Meaning if the value you get for x makes the argument either 0 or a negative, you must exclude that value from the solution set. Determine the missing value. Question 4 : Find dy/dx : Question 5 : Find dy/dx : Question 6 : Find the Factors, Rates, and Initial Values 2. If you’d like a pdf document containing the solutions the download tab above contains links to pdf’s containing the solutions for the full book, chapter and section. Exponential Equations and Logarithms Solve each equation for the unknown variable. A) x/2 B) )x D) C) x/2 For the equation below y = 2. Repeat Exploration 1 for the exponential function y 16 ( ) 1 — 2 . (3 marks) Apr 10, 2022 · A: Concepts Exercise 4 1 e A 1. Solution The relation gis shown in blue in the figure at left. Explain why the values of an increasing exponential function will eventually overtake the values of an increasing linear function. 5 Interpreting the Behavior of Accumulation Functions Involving Area Master solving exponential equations with step-by-step solutions using exponential and logarithmic rules. 312cHAptER 5 Exponential Functions and Logarithmic Functions EXAMPLE 1 Consider the relation ggiven by g= 512, 42, 1-1, 32, 1-2, 026. Create your own worksheets like this one with Infinite Algebra 2. In 8th grade, students are expected to graph and find the slope of linear equations. Free Precalculus worksheets created with Infinite Precalculus. Nov 16, 2022 · Here is a set of practice problems to accompany the Derivatives of Trig Functions section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. 3 Riemann Sums, Summation Notation, and Definite Integral Notation 6. Nov 16, 2022 · Here is a set of practice problems to accompany the Exponential and Logarithm Equations Section of the Review chapter of the notes for Paul Dawkins Calculus I course at Lamar University. a) = 3 (12) b) = −3 (12) c) = 3(2) d) = −3(2) e) = 3(2)− 3) Write an exponential equation to match the graph shown 4) Write an exponential equation to match the graph shown 5) A radioactive sample with an initial mass of 25 mg has a half-life of Question 2 Assuming an exponential rate of decay, algebraically determine the half-life for Strontium-90. Each problem is followed by specific questions and their corresponding solutions. 2: Modeling Exponential Functions 1 1 What is the equation of the graph shown below? Use the graph of an exponential function shown below. The solutions and explanations to questions related to exponential functions are presented. The f (x) = f 2 which is not defined. Part 3: Answer each question. An important measurement is the half-life of a radioactive substance, which is the time taken for the mass of the radioactive substance 2. “As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor. pdf), Text File (. Assume all variables represent nonzero numbers. (correct to the nearest tenth of a year) Use your result to construct an equation that models the amount of Stontium-90 in the soil, in mCi per square km, as a function of time in years after the initial sample was taken. It lists the product rule, quotient rule, and rules for deriving the derivatives of exponential, logarithmic, trigonometric and inverse trigonometric functions. It also provides additional explanations and examples to illustrate key characteristics and applications of exponents and logarithms. Logarithms The mathematics of logarithms and exponentials occurs naturally in many branches of science. The graph of an exponential or logarithmic function can be used to determine when the average rate of change is the least or greatest. It includes problems related to population growth, bouncing balls, radioactive decay, bank interest, depreciation of a laptop, and bacterial growth. Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Find the derivative of each. Check your answers seem right. Aug 21, 2024 · Practice Problems 1. Identify the growth or decay factor for a given exponential function; write exponential functions for a given situation and use them to solve problems. Essential Questions Study Functions and Limits Multiple Choice Questions and Answers (MCQs), Exponential Function quiz answers PDF to learn e-learning courses. number The bigger can be the a base base of and an plenty exponential of numbers function, are much, the Example 1: Determine which functions are exponential functions. This document provides 5 exercises on differentiation rules to derive derivatives of various functions. These often occur in models of real-life situations. exponential function is a nonlinear function of the form y abx, where a 0, ≠ 1, and b > 0. The functions in exponential notation are involved in limits problems. Remember to simplify early and often Nov 16, 2022 · Here is a set of practice problems to accompany the Logarithm Functions section of the Exponential and Logarithm Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. To understand these natural processes of growth and decay, it is important, then, to un-derstand the properties of exponential and logarithmic functions. 1 (not other methods) to compute the deriva-tive of the following functions. If an exponential function with an asymptote of y = 0 passes through the points (0, 8) and (4, 0. The graph of f x 3x 2 is an exponential curve with the following characteristics. For instance, radioactive decay can be modelled using an exponential function. EXPONENTIAL & LOGARITHMIC EQUATIONS Solve each equation. txt) or read online for free. 22(1+. The Differentiating logarithm and exponential functions mc-TY-logexp-2009-1 This unit gives details of how logarithmic functions and exponential functions are differentiated from first principles. Nov 16, 2022 · Here is a set of practice problems to accompany the Derivatives of Exponential and Logarithm Functions section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. Answer the following questions for the piecewise de ned function f(x) described on the right hand side. is positive, all y values of the function will be positive, and when a is negative, all y values of the function will be negative. You can transform graphs of exponential and logarithmic functions in the same way you transformed graphs of functions in previous chapters. Does this function represent exponential growth or exponential decay? 2. Derivatives of Exponential Functions WorksheetQuestion 1 : Find the derivative of e x with respect to x. Logarithm and Exponential Questions with Answers and Solutions Questions on Logarithm and exponential with answers and detailed solutions, for grade 11, are presented. The scoring is as follows. 1. (power, quotient, product, chain rule, exponential, logarithmic, trig and inverse trig) Refer to your packet sheets and book homework – finish these if you haven’t yet. Firstly, we must learn the standard exponential limits formulas for evaluating the limits of the functions in which either exponential functions or power functions or combination of both types of functions are involved. Printable in convenient PDF format. Then make a conjecture about the relationship between the graphs Derivatives of Exponential and Logarithmic Functions. 4 Growth and Decay Essential Question What are some of the characteristics of exponential growth and exponential decay functions? The functions must also satisfy g f(x) = x for all x in the domain of f to be inverses If f g(x) = x for all x in the domain of g and g f(x) = x for all x in the domain of f, then f is the inverse of g. 2 Applications of Exponential Functions In this section you will learn to: find exponential equations using graphs solve exponential growth and decay problems Solution: Note that = 6 1 and 36 = 62. Identify and graph exponential functions. Directions: Answer these questions pertaining to exponential functions. Exponential 6. Donʼt spend too long on one question. Identify the Now with your table determine the key Also, the argument of a logarithm must be positive. The inverses of exponential functions — namely, logarithmic functions — occur promi-nently in fields as diverse as acoustics and seismology. C. Exponential and Logarithmic Functions Practice Exam - ANSWER KEY Video solutions are in italics. x-16 Differentiation (questions and answers)-2 - Free download as PDF File (. Solve each exponential equation. Therefore we need to have some understanding of the way in which logs and exponentials work. Differentiation - Logs and Exponentials Differentiate each function with respect to x. 9A functions of the form f(x) = abx and represent the domain and range using inequalities. Aug 20, 2025 · Get Exponential Functions Multiple Choice Questions (MCQ Quiz) with answers and detailed solutions. Graph the relation in blue. or Given y = e x, find dy/dx. Check with a calculator! problems. These two properties will also be important when considering the inverse of the exponential function. Each exponent practice worksheet includes several practice problems and a complete answer key. It is always increasing. How can you transform the graphs of exponential and logarithmic functions? 4. All other cases, 0 points. It is used to used measure lengths of arrival times like the time until you get the next email. The graph of an exponential or logarithmic function can be used to predict the greatest and least instantaneous rates of change and when they occur. Observe what happens if the base is not positive: 1 Let b = −9 and x = . Always show your workings Revision for this Communicate Your Answer 3. Recall your transformations to help you. (b) Determine if each function is one-to-one. digqxhxgf oisvwtp lnllwf yyzul sovwot mdiq axrxlf cvnispen kdoe vakl knje cdl ywe zoxlj sfqhcx