(7.1 & 7.2) NOTES- Exponential Growth and Decay. Definition: Consider the exponential function: if 0 < a < 1: exponential decay if a > 1: exponential.

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(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)

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: _____________ /4 1/ y = 0

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

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

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

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

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: _____________ /3 1/9 1/31 1 y = 0

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

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

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

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

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

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 /16 1/ Left 1, down 3 1 y = -3

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 /4 1/16 1/4 Reflect x-axis, right 2, up 5

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 /4 1/16 1/4 Reflect x-axis, right 2, up y = 5