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(7.1 & 7.2) NOTES- Exponential Growth and Decay

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

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(7.1 & 7.2) NOTES- Exponential Growth and Decay

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  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: -2 1/4 -1 1/2 0 1 1 2 2 4 2 1 a=______ C= ______ (circle one) exponential decay or growth y- intercept: _________ equation of asymptote: __________ d: __________ r: _____________ 1 y = 0

  4. Transformations: Eq. of asymptote: Domain: Range: Left 3 y = 0

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

  6. Transformations: Eq. of asymptote: Domain: Range: Reflect in x-axis, up 3 y = 3

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

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

  9. Transformations: Eq. of asymptote: Domain: Range: Up 1 y = 1

  10. Transformations: Eq. of asymptote: Domain: Range: Down 3 y = -3

  11. Transformations: Eq. of asymptote: Domain: Range: Reflect in x-axis y = 0

  12. Transformations: Eq. of asymptote: Domain: Range: Reflect in x-axis, up 2 y = 2

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

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

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

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