University:
Boston University
Course:
GRS MA 742 | Algebra II
Academic year:

2024
Views:

99

Pages:

2
Author:

esfredint7qo

Chapter 3.2 Suggested Practice Problems Expected Skills: • Be able to graph y = bx for any base b > 0, b 6= 1. • Be able to apply graph transformations (reflections over x and/or y axes, vertical/horizontal shifts) to graph a given exponential function. • Be able to find the domain and range of an exponential function. • Be able to solve equations with exponential functions using the one-to-one property bx = by ⇐⇒ x = y. Textbook Practice Problems: • Section 3.2 #’s 13, 15, 19, 21, 23, 25, 27, 29, 33, 35, 39, 41 Additional Practice Problems: 1. Solve for x using the one-to-one property: 53−2x = 5−x 3 2. Solve for x using the one-to-one property: 8x−1 = 2x+2 5 2 3. Solve for x using the one-to-one property: 2x+1 = 16x+7 −9 4. Solve for x using the one-to-one property: −  x+2 1 = 3x−1 3 1 2 5. Solve for x using the one-to-one property: 85x = 163x+4 16 3 6. Solve for x using the one-to-one property: 64 · 16−3x = 163x−2 7 12 1 7. Solve for x using the one-to-one property: 4x 2 −x = 4 · 2x 2 −x 2 or −1 8. Consider the exponential equation 9x + 3 = 4(3x ). (a) Make a substitution u = 3x to convert this equation to a quadratic equation. What are the values of u that solve this equation? The resulting quadratic equation is u2 − 4x + 3 = 0 which has solutions u = 1 or u = 3. (b) Now use the result from part (a) to solve for x which satisfy the original equation. For u = 1, we solve 3x = 1 which gives x = 0. For u = 3, we solve 3x = 3, which gives x = 1. Thus, the original equation has solutions x = 0 and x = 1. 9. Make the substitution y = 2x to solve 4x + 2x = 20. 2 2

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