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Lesson 19 – Graphs of Exponential Functions

Lesson 19 – Graphs of Exponential Functions. Pre Calculus - Santowski. (A) Review of Exponent Laws. (B) Exponential Parent Functions. The features of the parent exponential function y = a x (where a > 1) are as follows:.

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Lesson 19 – Graphs of Exponential Functions

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  1. Lesson 19 – Graphs of Exponential Functions Pre Calculus - Santowski PreCalculus

  2. (A) Review of Exponent Laws PreCalculus

  3. (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: PreCalculus

  4. (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 → PreCalculus

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

  6. (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 PreCalculus

  7. (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) PreCalculus

  8. (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) PreCalculus

  9. (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) PreCalculus

  10. (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) PreCalculus

  11. (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 PreCalculus

  12. (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 PreCalculus

  13. (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: PreCalculus

  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 PreCalculus 14

  15. 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 PreCalculus

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