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 yintercept 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 yintercept 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 onetoone function? b.) Why is it important to know whether or not the function is onetoone? 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 onetoone function b.) because onetoone 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.) yintercept: (0, 1) b.) increasing c.) as x decreases without bound, f(x) approaches 0 d.) the xaxis 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 xaxis 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.) yintercept: (0, 1) b.) decreasing c.) as x increases without bound, f(x) approaches 0 d.) the xaxis is a horizontal asymptote 4 6 Answer Key Testname: 3.2 EXPONENTIAL FUNCTIONS 8. First reflect the graph of f across the xaxis 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 xaxis.
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.
 Spring '08
 MatRoy
 Exponential Function, Exponential Functions

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