9/4/2015 PreCalculus 1 Lesson 19 – Graphs of Exponential Functions Pre Calculus - Santowski

(A) Review of Exponent Laws 9/4/2015 PreCalculus 2

(B) Exponential Parent Functions The features of the parent exponential function y = a x (where a > 1) are as follows: The features of the parent exponential function y = a -x (where a > 1) are as follows: 9/4/2015 PreCalculus 3

(B) Exponential Parent Functions The features of the parent exponential function y = a x (where a > 1) are as follows: Domain  Range  Intercept  Increase/decrease on  Asymptote  As x →-∞, y → As x → ∞, y → The features of the parent exponential function y = a -x (where a > 1) are as follows: Domain  Range  Intercept  Increase/decrease on  Asymptote  As x →-∞, y → As x → ∞, y → 9/4/2015 PreCalculus 4

(C) Transforming Exponential Functions Recall what information is being communicated about the function y = f(x) by the transformational formula 9/4/2015 PreCalculus 5

(C) Transforming Exponential Functions – Calculator Explorations Use DESMOS to compare the graphs of: (i) y = 2 x (ii) y = 2 2x (iii) y = 2 3x (iv) y = 2 0.2x (v) y = 2 0.6x Use DESMOS to compare the graphs of: (i) y = 4×2 x (ii) y = -2×2 x (iii) y = 0.2×2 x (iv) y = ( ⅙ )×2 x (v) y = 10×2 x 9/4/2015 PreCalculus 6

(C) Transforming Exponential Functions Graph f(x) = 2 x List 3 key points on the parent function Draw the asymptote and label the intercept(s) Graph g(x) = 4 – 2 x List the transformations applied to f(x) List 3 key points on the parent function Solve g(x) = 0 and evaluate g(0) Draw the asymptote and label the intercept(s) 9/4/2015 PreCalculus 7

(C) Transforming Exponential Functions Graph h(x) = 2 x+3 List the transformations applied to f(x) List 3 key points on the new function Solve h(x) = 0 & evaluate h(0) Draw the asymptote and label the intercept(s) Graph k(x) = 8(2 x ) and explain WHY the two graphs are equivalent Graph List the transformations applied to f(x) List 3 key points on the new function Solve m(x) = 0 and evaluate m(0) Draw the asymptote and label the intercept(s) 9/4/2015 PreCalculus 8

(C) Transforming Exponential Functions Graph A(x) = ½ x Explain WHY ½ x = 2 -x. List the transformations applied to f(x) List 3 key points on the parent function Draw the asymptote and label the intercept(s) Graph B(x) = 2 – 0.5 x List the transformations applied to f(x) List 3 key points on the new function Solve B(x) = 0 and evaluate B(0) Draw the asymptote and label the intercept(s) 9/4/2015 PreCalculus 9

(C) Transforming Exponential Functions Graph C(x) = 2 3-x List the transformations applied to f(x) List 3 key points on the new function Solve C(x) = 0 and evaluate C(0) Draw the asymptote and label the intercept(s) Graph List the transformations applied to f(x) List 3 key points on the new function Solve D(x) = 0 and evaluate D(0) Draw the asymptote and label the intercept(s) 9/4/2015 PreCalculus 10

(D) Exploring Constraints Provide mathematical based explanations or workings to decide if f(x) = -2 x is/is not a function Provide mathematical based explanations or workings to decide if f(x) = (-2) x is/is not a function 9/4/2015 PreCalculus 11

(E) Other Exponential Functions Analyze the end behaviours and intercepts of the functions listed below. Then graph each function on your GDC (A) Logistic Functions (B) Catenary Functions 9/4/2015 PreCalculus 12

(F) Working with Parameters You will be divided into groups and each group will investigate the effect of changing the parameters on the characteristics of the function and prepare a sketch of Where: 9/4/2015 PreCalculus 13 GroupaZbcd 1 a > 1 Z > 1 b > 1 c > 0 d > 0 2 a < -1 Z > 1 0 < b < 1 c < 0 d > < a < 1 Z > 1 b < -1 c > 0 d > < a < 0 Z > 1 -1 < b < 0 c > 0 d < 0 5 a > 1 Z > 1 b < -1 c < 0 d < 0

9/4/2015 PreCalculus 14 (G) Exponential Modeling Investments grow exponentially as well according to the formula A = P o (1 + i) n. If you invest $500 into an investment paying 7% interest compounded annually, what would be the total value of the investment after 5 years? You invest $5000 in a stock that grows at a rate of 12% per annum compounded quarterly. The value of the stock is given by the equation V = 5000( /4) 4x, or V = 5000(1.03) 4x where x is measured in years.  (a) Find the value of the stock in 6 years.  (b) Find when the stock value is $14,000

Homework Finish the questions on Slides #8,9,10 From the HOLT PreCalculus – A Graphing Approach, Sec 5.2, p343-5, Q1,3,5,7,9,11,13,15,17,19,20,21,45,47,51,54 9/4/2015 PreCalculus 15