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General Form and Graph for an Exponential Function

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A function whose input (x) is located in the exponent. Example: Jason has $17 and quadruples his money every month. Write an equation to represent the situation. Exponential Equation Initial Multiplier

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Exponential Table There is a constant MULTIPLIER between consecutive output values. XY 5.67 017 151 2153 3459 x3

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For any Exponential: Graphs of y=b x 0 < b < 1 b = 1 b > 1 Increasing, asymptote y=0 Decreasing, asymptote y=0 Horizontal line y=1 Domain: x-intercept(s): y-intercept(s): Vertical asymptote: None (0,1) b > 0 Range:

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Representations of y=ab x xy=a(b)xy=a(b)x -3 -2 0 1 2 The initial value The multiplier a (0,a) Context: a is the starting point b is the multiplier x b

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Why b>0 in y=b x xy=(-2) x -3 -2 0 1 2 3 4 -.125.25 -.5 1 -2 4 -8 16 UGLY GRAPH!

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What is the symmetry? f(x)= x 3 –x.

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