8-2A: Properties of Exponential Functions
Objectives:
• To graph exponential functions.
• To graph translations of exponential functions.
• To write an exponential equation for a translation given the parent function and a shift description.
Process:
(1) Identify the parent function.
(2) Complete the middle two columns of the x/y table for the parent (do not graph the parent).
(3) Describe the transformation (shifts left/right, shifts up/down, opens up/down).
**Remember: "x lies, y tells the truth**
(4) Fill out the x/y table for the child based on the transformation information.
(5) Graph ONLY the child data.
(6) Identify and graph the asymptote with a dotted line (label it with y = ).
(7) Identify the y­intercept (sometimes you will have to solve for it).
Graphing Exponential Growth and Decay
parent:
transformation:
asymptote:
y­intercept:
child:
Remember:
"x lies,
y tells the truth"!
parent:
child:
transformation:
asymptote:
y­intercept:
parent:
transformation:
asymptote:
y­intercept:
child:
child:
parent:
transformation:
asymptote:
y­intercept:
Given a "parent" graph and a shift description, write an equation for the "child".
>
Write an equation for the "parent" graph:
<
y = 0
Now, use the parent function with this shift description to write an equation for the "child": right 8, up 2.
>
Practice Problem:
Write an equation for the "parent" graph:
y = 0
<
Now, use the parent function with this shift description to write an equation for the "child": left 7, down 3.