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

Answer:

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

$g(x)=(3)^{5x}$; Horizontal compression

$p(x)=\frac{1}{2}(3)^x$; Vertical compression

$w(x)=(3)^{0.2x}$; Horizontal stretch

Step-by-step 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.

$p(x)=\frac{1}{2}(3)^x$

$p(x)=\frac{1}{2}f(x)$

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.