Question

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

Answer 1

Answer:

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

Step-by-step explanation:

If the graph of the function $y=f(hx)$  represents the transformations made to the graph of $y= f(x)$  then, by definition:

If $0$ the graph is stretched horizontally  by a factor $\frac{1}{h}$

If $h> 1$ the graph is compressed horizontally by a factor $\frac{1}{h}$

In this problem we have the parent function $y=x^2$ And we know that it stretches horizontally by a factor of 4

Therefore

$0$  and $h=\frac{1}{4}$

The transformation is:

$y=f(\frac{1}{4}x)$

And the function is:

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