1. (7.1 & 7.2) NOTES- Exponential Growth and Decay

2. Definition: Consider the exponential function: if 0 < a < 1: exponential decay if a > 1: exponential growth Asymptote: A line that a graph approaches, but never reaches (boundary line)

3. Ex: Graph the given exponential function using a table and identifying the following: xy a=______ C= ______ (circle one) exponential decay or growth y- intercept: _________ equation of asymptote: __________ d: __________ r: _____________ -2 0 1 2 1/4 1/2 1 2 4 21 1 y = 0

4. Transformations: Eq. of asymptote: Domain: Range: Left 3 y = 0 yx -2 0 1 2 1/4 1/2 1 2 4

5. Transformations: Eq. of asymptote: Domain: Range: Right 2, down 4 y = -4 yx -2 0 1 2 1/4 1/2 1 2 4

6. Transformations: Eq. of asymptote: Domain: Range: Reflect in x-axis, up 3 y = 3 yx -2 0 1 2 1/4 1/2 1 2 4

7. Transformations: Eq. of asymptote: Domain: Range: Right 2, down 1 y = -1 yx -2 0 1 2 1/4 1/2 1 2 4

8. Ex: Graph the given exponential function using an x/y-chart and identify the following: xy a=______ C= ______ (circle one) exponential decay or growth y- intercept: _________ equation of asymptote: __________ d: __________ r: _____________ -2 0 1 2 9 3 1 1/3 1/9 1/31 1 y = 0

9. Transformations: Eq. of asymptote: Domain: Range: Up 1 y = 1 yx -2 0 1 2 9 3 1 1/3 1/9

10. Transformations: Eq. of asymptote: Domain: Range: Down 3 y = -3 yx -2 0 1 2 9 3 1 1/3 1/9

11. Transformations: Eq. of asymptote: Domain: Range: Reflect in x-axis y = 0 yx -2 0 1 2 9 3 1 1/3 1/9

12. Transformations: Eq. of asymptote: Domain: Range: Reflect in x-axis, up 2 y = 2 yx -2 0 1 2 9 3 1 1/3 1/9

13. Consider the parent equation, and transformed equation IN GENERAL, the following transform the graph of by: h shifts: _______________ k shifts: _______________ reflects: _______________ Left or right Up or down x-axis

14. equation of parent graph: ___________ a=_____ C= _____ (circle one) exponential decay or growth transformations: _______________________ y-intercept: ____________ equation of asymptote: _________________ domain: _______________ range: _______________ Ex: Graph the exponential function: xy -2 0 1 2 1/16 1/4 1 4 16 41 Left 1, down 3 1 y = -3

15. equation of parent graph: ___________ a=_____ C= _____ (circle one) exponential decay or growth transformations: _____________________________________ y-intercept: ____________ equation of asymptote: _________________ domain: _______________ range: _______________ Ex: Graph the exponential function: xy -2 0 1 2 16 4 1 1/4 1/16 1/4 Reflect x-axis, right 2, up 5

16. equation of parent graph: ___________ a=_____ C= _____ (circle one) exponential decay or growth transformations: _____________________________________ y-intercept: ____________ equation of asymptote: _________________ domain: _______________ range: _______________ Ex: Graph the exponential function: xy -2 0 1 2 16 4 1 1/4 1/16 1/4 Reflect x-axis, right 2, up 5 -11 y = 5