3.2 Exponential Functions-ANSWER KEY

3.2 Exponential Functions-ANSWER KEY - Name 3.2 Exponential...

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Unformatted text preview: Name___________________________________ 3.2: Exponential Functions The exponential function with base b is defined by f(x) = bx where b > 0, b 1, and x is a real number. 1. Evaluate f(x) = 3 x at x = 4, x = -3, and x = 5 Sketch the graph of the exponential function by completing the table. Round to two decimal places, if necessary. 2. f(x) = 4 x 16 14 12 10 8 y x f(x) -3 -2 -1 0 1 2 6 4 2 -8 -6 -4 -2 -2 2 4 6 8 x a.) What is the y-intercept of the graph? b.) Following the graph from left to right, is this function increasing or decreasing? c.) What happens to f(x) as x decreases without bound (that is, as x -)? d.) Does the function f have an asymptote? If so, what is it? Sketch the graph of the exponential function by completing the table. Round to two decimal places, if necessary. 3. f(x) = 3 x 5 y 8 6 x f(x) -3 -2 -1 0 1 2 4 2 -4 -2 -2 2 4 x a.) What is the y-intercept of the graph? b.) Following the graph from left to right, is this function increasing or decreasing? b.) What happens to f(x) as x increases without bound (that is, as x )? c.) Does the function f have an asymptote? If so, what is it? Answer the following questions. Refer to section 3.2 (p. 218) in your textbook. 4. For any exponential function f(x) = bx, where the base b is a positive real number and b 1: a.) Is f always a one-to-one function? b.) Why is it important to know whether or not the function is one-to-one? c.) What is the domain of the function f? What is the range of the function f? For all real numbers x, the function defined by f(x) = ex is called the natural exponential function. 5. Use your calculator to write the value of the number e, accurate to five decimal places. e 1 Sketch the graph of the exponential function by completing the table. Round to two decimal places, if necessary. 6. f(x) = ex y 8 6 x f(x) -3 -2 -1 0 1 2 4 2 -4 -2 -2 2 4 6 x a.) Following the graph from left to right, is this function increasing or decreasing? b.) What happens to f(x) as x decreases without bound (that is, as x -)? c.) Does the function f have an asymptote? If so, what is it? Answer the following. Refer to section 1.6 (p. 85 -87) in your textbook. 7. Explain how to graph the function F(x) below, using translation or reflection on the given function f. Then sketch a graph of both functions. f(x) = 4 x , F(x) = 4 x + 3 8. Explain how to graph the function g(x) below, using translation or reflection on the given function f. Then sketch a graph of both functions. f(x) = ex , g(x) = - ex - 2 9. Explain how to graph the function h(x) below, using translation or reflection on the given function f. Then sketch a graph of both functions. f(x) = ex , h(x) = - e (x - 4) Answer Key Testname: 3.2 EXPONENTIAL FUNCTIONS 1. f(4) = 81, f(-3) = 1 , f( 5) = 11.66475 27 4. a.) yes, f is always a one-to-one function b.) because one-to-one functions are invertible 2. y 14 12 10 8 6 4 2 -8 -6 -4 -2 -2 2 4 6 8x c.) the domain of f is the set of real numbers; the range of f is the set of positive real numbers 5. e 2.71828 6. y 6 4 a.) y-intercept: (0, 1) b.) increasing c.) as x decreases without bound, f(x) approaches 0 d.) the x-axis is a horizontal asymptote 3. y 6 -4 -2 2 2 -2 4 x b.) increasing c.) as x decreases without bound, f(x) approaches 0 d.) the x-axis is a horizontal asymptote 7. Shift the graph of f vertically upward 3 units. y 4 2 6 4 -4 -2 -2 2 4 x -6 -4 -2 2 2 -2 4 6 x a.) y-intercept: (0, 1) b.) decreasing c.) as x increases without bound, f(x) approaches 0 d.) the x-axis is a horizontal asymptote -4 -6 Answer Key Testname: 3.2 EXPONENTIAL FUNCTIONS 8. First reflect the graph of f across the x-axis and then shift this graph vertically downward 2 units. 6 4 2 -6 -4 -2 -2 -4 -6 2 4 6 x y 9. First shift the graph of f horizontally right 4 units then reflect across the x-axis. 6 4 2 -6 -4 -2 -2 -4 -6 2 4 6 x y ...
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This note was uploaded on 04/13/2008 for the course MATH 2412 taught by Professor Matroy during the Spring '08 term at Alamo Colleges.

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