4-7 Transforming Exponential and Logartimic Functions
Obj: To transform exponential and logarithmic functions by changing parameters.
(WHY? – Psychologists can use transformations of exponential functions to describe knowledge retention rates over time – ex 5)
The same transformations that we applied to quadratic, linear, and polynomial functions
can be performed on exponential and logarithmic functions. See below.
Ex 1. Translating Exponential Functions –
Graph the function 𝑔(𝑥 ) = 2𝑥 − 4 AND name the y-intercept and asymptote
(hint: Graph 𝑔(𝑥) = 2𝑥 𝑢𝑠𝑖𝑛𝑔 − 2, −1, 0, 1, 2, THEN translate the graph)
Ex. 2 Stretching and Reflecting Exponential Functions
Graph the following
𝑔(𝑥) = 2(3)2
Name the y-intercept and asymptote
1
ℎ(𝑥) = − (2𝑥 )
4
Name the y-intercept and asymptote
Ex 3 – Transforming Logarithmic functions
Graph the following:
𝑞(𝑥) = ln(𝑥 − 4)
Name the y-intercept and asymptote
Ex 4. - Writing Transformed functions
Write the transformed function
𝑓(𝑥 ) = 0.2𝑥 is translated 2 units to the right, compressed vertically by a factor
1
of , and reflected across the x-axis.
3