Question

The functions below are transformations of the parent function f(x) = 3x . Match each function to it's correct transformation. Question 24 options:

h(x) = 4(3)x

g(x) = (3)5x

p(x) = 12(3)x

w(x) = 30.2x

1. Vertical Stretch

2. Vertical Compression

3. Horizontal Stretch

4. Horizontal Compression

Answer 1

`h(x)=4(3)^x`; Vertical stretch

`g(x)=(3)^(5x)`; Horizontal compression

`p(x)=(1)/(2)(3)^x`; Vertical compression

`w(x)=(3)^(0.2x)`; Horizontal stretch

Explanation:

The given parent function is

`f(x)=3^x`

The transformation between two functions is defined as

`q(x)=kf(x)`

If 0<k<1, then it is vertical compression and k>1 then it is vertical stretch.

`q(x)=f(jx)`

If 0<j<1, then it is horizontal stretch and j>1 then it is horizontal compression.

`h(x)=4(3)^x`

`h(x)=4f(x)`

Here, k=4, therefore it is vertical stretch.

`g(x)=(3)^(5x)`

`g(x)=f(5x)`

Here, j=5, therefore it is horizontal compression.

`p(x)=(1)/(2)(3)^x`

`p(x)=(1)/(2)f(x)`

Here, k=1/2, therefore it is vertical compression.

`w(x)=(3)^(0.2x)`

`w(x)=f(0.2x)`

Here, j=0.2, therefore it is horizontal stretch.