Intercepts, Exponentials, and Asymptotes Section 3.4 Standard: MCC9-12.F.IF.7a&e Essential Question: How do you graph and analyze exponential functions.

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Intercepts, Exponentials, and Asymptotes Section 3.4 Standard: MCC9-12.F.IF.7a&e Essential Question: How do you graph and analyze exponential functions and their inverses?

Vocabulary: Exponential function: a function of the form y = ab x where a ≠ 0 and the base b is a positive number other than 1 Exponential decay function: a function of the form y = ab x where a > 0 and 0 < b < 1 Exponential growth function: a function of the form y = ab x where a > 0 and b > 1 Growth or decay factor: b in the function y = ab x Asymptote: a line that a graph approaches more and more closely End behavior: the behavior of the graph as x approaches positive and negative infinity.

Remember how to find the x- and y- intercepts of a function: To find the x-intercept, let y = 0 and solve for x. To find the y-intercept, let x = 0 and solve for y.

Example 1: a.Find the x-intercept for this function. b.Find the y-intercept for this function.

Example 2: a.Find the x-intercept for this function. b.Find the y-intercept for this function.

Example 3: a.Find the x-intercept for this function. b.Find the y-intercept for this function. xy

Example 4: a.Find the x-intercept for this function. b.Find the y-intercept for this function. xf(x)

5) Graph y = 3 x xy Growth

Domain: Range: Asymptote: y-intercept: Interval of increasing: Interval of decreasing: End behavior:

6) Graph. xy Decay

Domain: Range: Asymptotes: Y-intercept: Interval of increasing: Interval of decreasing: End behavior:

7) Graph xy Growth

Domain: Range: Asymptotes: Y-intercept: Interval of increasing: Interval of decreasing: End behavior:

8) Graph xy Growth

Domain: Range: Asymptotes: Y-intercept: Interval of increasing: Interval of decreasing: End behavior: