Lesson 19 Graphs of Exponential Functions Pre Calculus

Lesson 19 – Graphs of Exponential Functions Pre Calculus - Santowski 1/26/2022 Pre. Calculus 1

(A) Review of Exponent Laws n 1/26/2022 Pre. Calculus 2

(B) Exponential Parent Functions n The features of the parent exponential function y = ax (where a > 1) are as follows: 1/26/2022 n Pre. Calculus The features of the parent exponential function y = a-x (where a > 1) are as follows: 3

(B) Exponential Parent Functions n The features of the parent exponential function y = ax (where a > 1) are as follows: n The features of the parent exponential function y = a-x (where a > 1) are as follows: n Domain Range Intercept Increase/decrease on Asymptote As x →-∞, y → As x → ∞, y → n n n 1/26/2022 n n n Pre. Calculus 4

(C) Transforming Exponential Functions n Recall what information is being communicated about the function y = f(x) by the transformational formula 1/26/2022 Pre. Calculus 5

(C) Transforming Exponential Functions – Calculator Explorations n n n Use DESMOS to compare the graphs of: (i) y = 2 x (ii) y = 22 x (iii) y = 23 x (iv) y = 20. 2 x (v) y = 20. 6 x 1/26/2022 n n n Pre. Calculus 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 6

(C) Transforming Exponential Functions n n n Graph f(x) = 2 x n Graph g(x) = 4 – 2 x List 3 key points on the parent function n Draw the asymptote and label the intercept(s) n 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) 1/26/2022 n n Pre. Calculus 7

(C) Transforming Exponential Functions n Graph h(x) = 2 x+3 n 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 n n 1/26/2022 n Graph n 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) n n n Pre. Calculus 8

(C) Transforming Exponential Functions n n n Graph A(x) = ½x Explain WHY ½x = 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) 1/26/2022 n Graph B(x) = 2 – 0. 5 x n 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) n n n Pre. Calculus 9

(C) Transforming Exponential Functions n Graph C(x) = 23 -x n Graph n 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) n 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) n n n 1/26/2022 n n n Pre. Calculus 10

(D) Exploring Constraints n Provide mathematical based explanations or workings to decide if f(x) = -2 x is/is not a function n Provide mathematical based explanations or workings to decide if f(x) = (-2)x is/is not a function 1/26/2022 Pre. Calculus 11

(E) Other Exponential Functions n Analyze the end behaviours and intercepts of the functions listed below. Then graph each function on your GDC n (A) Logistic Functions n (B) Catenary Functions 1/26/2022 Pre. Calculus 12

(F) Working with Parameters n 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 n Where: Group a Z b c d 1 a>1 Z>1 b>1 c>0 d>0 2 a < -1 Z>1 0<b<1 c<0 d>0 3 0<a<1 Z>1 b < -1 c>0 d>0 4 -1 < a < 0 Z>1 -1 < b < 0 c>0 d<0 5 a>1 Z>1 b < -1 c<0 d<0 1/26/2022 Pre. Calculus 13

(G) Exponential Modeling n Investments grow exponentially as well according to the formula A = Po(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? n 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(1 + 0. 12/4)4 x, or V = 5000(1. 03)4 x where x is measured in years. q (a) Find the value of the stock in 6 years. q (b) Find when the stock value is $14, 000 1/26/2022 Pre. Calculus 14 14

Homework n Finish the questions on Slides #8, 9, 10 n From the HOLT Pre. Calculus – A Graphing Approach, Sec 5. 2, p 343 -5, Q 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 21, 45, 47, 51, 54 1/26/2022 Pre. Calculus 15