1. 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?

2. 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.

3. 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.

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

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

6. Example 3: a.Find the x-intercept for this function. b.Find the y-intercept for this function. xy -2 0 02 14 26

7. Example 4: a.Find the x-intercept for this function. b.Find the y-intercept for this function. xf(x) -2-9 0-6 2-3 40 63

8. 5) Graph y = 3 x. -8 -6 -4 -2 2 4 6 8 86428642 -2 -4 -6 -8 xy Growth

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

10. 6) Graph. xy Decay -8 -6 -4 -2 2 4 6 8 86428642 -2 -4 -6 -8

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

12. 7) Graph. -8 -6 -4 -2 2 4 6 8 86428642 -2 -4 -6 -8 xy Growth

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

14. 8) Graph. -16 -12 -8 -4 4 8 12 16 16 12 8 4 -4 -8 -12 -16 xy Growth

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