Question

If you horizontally stretch the quadratic parent function f(x) = x^2 by a factor of 4 what’s the equation of the new function

Answer 1

Answer:

Horizontal stretch:

If a parent function y = f(x) ,

Replace x with $\frac{x}{n}$ result in horizontal stretch by a factor of n.

then a new function become $g(x) = f(\frac{x}{n})$

As per the statement:

Horizontally stretch the quadratic parent function $f(x) = x^2$ by a factor of 4 .

By definition of Horizontal stretch:

A equation of new function become:

$g(x) = f(\frac{x}{4})=(\frac{x}{4})^2=\frac{1}{16}x^2$

therefore, a equation of the new function is, $g(x) = \frac{1}{16}x^2$

Answer 2

F'(x)=(x/4)^2 or (x^2)/16