Question

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). f(x) = 4 cos x ; g(x) = cos x
Select one:
a. Vertical stretch by a factor of 4
b. Horizontal stretch by a factor of 4
c. Vertical shrink by a factor of 1/4
d. Horizontal shrink by a factor of 1/4

Answer 1

Answer:

Option a

Step-by-step explanation:

If the graph of the function $y=f(x)=cg(hx)$  represents the transformations made to the graph of $y= g(x)$  then, by definition:

If  $0 <c <1$ then the graph is compressed vertically by a factor c.

If  $|c| > 1$ then the graph is stretched vertically by a factor c

If $c <0$  then the graph is reflected on the x axis.

If $0 <h <1$ the graph is stretched horizontally  by a factor $\frac{1}{h}$

If $h> 1$ the graph is compressed horizontally by a factor $\frac{1}{h}$

In this problem we have the function $f(x)=4cos(x)$ and our parent function is $g(x)= cosx$

therefore it is true that  $c=4$   so $c>1$ and $h =1$

Therefore the graph of $y=cosx$ is stretched vertically by a factor c = 4

The answer is "Vertical stretched by a factor of 4"

Answer 2

C Vertical shrink by a factor of 1/4