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8-2 Properties of Exponential Functions. The function f(x) = b x is the parent of a family of exponential functions for each value of b. The factor a.

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Presentation on theme: "8-2 Properties of Exponential Functions. The function f(x) = b x is the parent of a family of exponential functions for each value of b. The factor a."— Presentation transcript:

1 8-2 Properties of Exponential Functions

2 The function f(x) = b x is the parent of a family of exponential functions for each value of b. The factor a in y = ab x stretches, shrinks, and/or reflects the parent. SummaryFamilies of Exponential Functions Parent functions (b > 0, b = 1): y = b x Stretch (|a| > 1) Shrink (0 < |a| < 1) Reflection (a < 0) in x-axis Translation (horizontal by h; vertical by k): y = b x-h + k Combined: y = ab x-h + k y = ab x }

3 example 1: Graphing y = ab x for 0<a<1 Graph y = and y =. Label the asymptote of each graph. Step 1 Make a tableStep 2 Graph the function x -2 0 1 2 3 x The y-intercept is a, or ½ The asymptote is y = 0 for both graphs The y-intercept is a, or ½

4 example 2: Translating y = ab x Graph the stretch y = 8(½) x and then the translation y = 8(½) x + 2 + 3. Step 1 Graph y = 8(½) x. The horizontal asymptote is y = 0. Step 2 For y = 8(½) x + 2 + 3, h = -2 and k = 3. So shift the y = 8(½) x graph 2 units left and 3 units up. The horizontal asymptote is y = 3. x

5 Class Work 8-2 Graph each function. 1. y = -4(2) x 2. y = -3 x 3. Graph the stretch y = 9(3) x 4. y = 9(3) x+1 5. y = 9(3) x-3 – 1


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