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Lesson 19 – Graphs of Exponential Functions

Pre Calculus - Santowski

(A) Review of Exponent Laws

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(B) Exponential Parent Functions The features of the parent

exponential function y = ax (where a > 1) are as follows:

The features of the parent exponential function y = a-x (where a > 1) are as follows:

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(B) Exponential Parent Functions The features of the parent

exponential function y = ax (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 →

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(C) Transforming Exponential Functions Recall what information is being

communicated about the function y = f(x) by the transformational formula

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dcxbafy

(C) Transforming Exponential Functions – Calculator Explorations Use DESMOS to

compare the graphs of:

(i) y = 2x

(ii) y = 22x

(iii) y = 23x

(iv) y = 20.2x

(v) y = 20.6x

Use DESMOS to compare the graphs of:

(i) y = 4×2x

(ii) y = -2×2x

(iii) y = 0.2×2x

(iv) y = (⅙)×2x

(v) y = 10×2x

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(C) Transforming Exponential Functions Graph f(x) = 2x

List 3 key points on the parent function

Draw the asymptote and label the intercept(s)

Graph g(x) = 4 – 2x

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)

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(C) Transforming Exponential Functions Graph h(x) = 2x+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(2x) 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)

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mx( ) =4−8 2( )x+2

(C) Transforming Exponential Functions 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)

Graph B(x) = 2 – 0.5x

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)

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(C) Transforming Exponential Functions Graph C(x) = 23-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)

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D x( ) =−2 0.5( )3x

(D) Exploring Constraints

Provide mathematical based explanations or workings to decide if f(x) = -2x is/is not a function

Provide mathematical based explanations or workings to decide if f(x) = (-2)x is/is not a function

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(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

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f x( ) =5

1+3⋅2−x2

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f x( ) =10 20.4x+2−0.4x( )

(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:

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daZy cxb

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

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(G) Exponential Modeling

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?

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)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

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