Question

If f(x) = x^2 is vertically compressed by a factor of 8 to g(x) what is the equation of g(x)?

A.
`g(x) = (1)/(8)x^2`

B.
`g(x) = (8x)^2`

C.
`g(x)=((1)/(8)x)^2`

D.
`g(x) = 8x^2`

Answer 1

Answer: First option

`g(x) = (1)/(8)x^2`

Explanation:

Step-by-step explanation:

If the graph of the function
`y=cf(x)` represents the transformations made to the graph of
`y= f(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.

In this problem we have the function
`f(x)=x^2` If this function is vertically compressed by a factor of 8 then
`0 <c <1` and
`c=(1)/(8)`

Therefore the graph of g(x) is
`g(x)=(1)/(8)f(x)`

`g(x) = (1)/(8)x^2`

The answer is the first option