(7.1 & 7.2) NOTES- Exponential Growth and Decay

Definition: Consider the exponential function: if 0 < a < 1: exponential decayif a > 1: exponential growthAsymptote:A line that a graph approaches, but never reaches (boundary line)

Ex: Graph the given exponential function using a table and identifying the following: a=______ C= ______(circle one) exponential decay or growthy- intercept: _________equation of asymptote: __________

d: __________ r: _____________-2-10121/41/2124211y = 0

xy

Transformations:

Eq. of asymptote:

Domain:

Range: Left 3y = 0

Transformations:

Eq. of asymptote:

Domain:

Range: Right 2, down 4y = -4

Transformations:

Eq. of asymptote:

Domain:

Range: Reflect in x-axis, up 3y = 3

Transformations:

Eq. of asymptote:

Domain:

Range: Right 2, down 1y = -1

Ex: Graph the given exponential function using an x/y-chart and identify the following: a=______ C= ______(circle one) exponential decay or growthy- intercept: _________equation of asymptote: __________

d: __________ r: _____________-2-10129 311/31/91/311y = 0

xy

Transformations:

Eq. of asymptote:

Domain:

Range: Up 1y = 1

Transformations:

Eq. of asymptote:

Domain:

Range: Down 3y = -3

Transformations:

Eq. of asymptote:

Domain:

Range: Reflect in x-axisy = 0

Transformations:

Eq. of asymptote:

Domain:

Range: Reflect in x-axis, up 2y = 2

Consider the parent equation, and

transformed equation

IN GENERAL, the following transform the graph of by:

h shifts: _______________

k shifts: _______________

reflects: _______________ Left or rightUp or downx-axis

equation of parent graph: ___________ a=_____ C= _____(circle one) exponential decay or growthtransformations: _______________________y-intercept: ____________equation of asymptote: _________________domain: _______________ range: _______________Ex: Graph the exponential function: -2-10121/161/4141641Left 1, down 31y = -3

xy

equation of parent graph: ___________ a=_____ C= _____(circle one) exponential decay or growthtransformations: _____________________________________y-intercept: ____________equation of asymptote: _________________domain: _______________ range: _______________Ex: Graph the exponential function: -2-1012 16 411/41/161/4-1Reflect x-axis, right 2, up 5

xy

equation of parent graph: ___________ a=_____ C= _____(circle one) exponential decay or growthtransformations: _____________________________________y-intercept: ____________equation of asymptote: _________________domain: _______________ range: _______________Ex: Graph the exponential function: -2-1012 16 411/41/161/4-1Reflect x-axis, right 2, up 5-11y = 5

xy