Question

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

Answer 1

Answer:

$r(x)=(4x)^7$

Step-by-step explanation:

• For a horizontal compression, we multiply whole numbers greater than 1 in front of $x$ of the given function.
• For horizontal expansion, we multiply by the reciprocal of the number for horizontal compression, in front of $x$ of the function.

For example,

If we wanted to horizontally compress $y=x^2$, we would multiply by 4 to get $y=(4x)^2$, and

if we wante to horizontally expand $y=x^2$, we would multiply by $\frac{1}{4}$ to get $y=(\frac{1}{4}x)^2$

Since this question asks for horizontal compression, we multiply the $x$ of the function by 4. So the function we need is $f(x)=(4x)^7$. The second choice is correct.