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

C Vertical shrink by a factor of 1/4

Answer 2

Option a

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
`(1)/(h)`

If
`h> 1` the graph is compressed horizontally by a factor
`(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"