Question

Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4?

q(x)=(1/4x)^7
r(x)=(4x)^7
s(x)=4x^7
t(x)=1/4x^7

thank you!

Answer 1

The answer is r(x) = (4x)^7

Answer 2

Note that what we want is to compress any point (a, b) in the parent function, to (a, b/4).

(a, b) is a point of the graph of the function
`f(x)=x^7`, thus we can rewrite the point as:

`(a, a^7)`.

This point is compressed to


`\displaystyle{ (a, (a^7)/(4) )`.

This means that the function we are looking for is
`\displaystyle{ t(x)= (x^7)/(4)`.

Answer: t(x)=1/4x^7