Lesson 19 – Graphs of Exponential Functions
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Transcript of Lesson 19 – Graphs of Exponential Functions
04/19/23 PreCalculus 1
Lesson 19 – Graphs of Exponential Functions
Pre Calculus - Santowski
(A) Review of Exponent Laws
04/19/23 PreCalculus 2
(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:
04/19/23 PreCalculus 3
(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 →
04/19/23 PreCalculus 4
(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
04/19/23 PreCalculus 6
(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)
04/19/23 PreCalculus 7
(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)
04/19/23 PreCalculus 8
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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)
04/19/23 PreCalculus 9
(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)
04/19/23 PreCalculus 10
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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:
04/19/23 PreCalculus 13
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
04/19/23 PreCalculus 14 14
(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
04/19/23 PreCalculus 15