Question

Identify the equation of the parent function y=x^3 that is horizontally streched by a factor of 1/5 and reflected over the y axis

Answer 1

Answer:

$y=\frac{-x^{3}}{125}$

Step-by-step explanation:

As we know that,

'Horizontal stretch, stretches the function left or right on the x-axis'.

The general form of horizontal stretch is given by 'f(kx)', where 0<k<1 is the factor by which function is stretched horizontally.

Since, the function $y=x^{3}$ which is stretched by a factor of $\frac{1}{5}$.

The new function is $y=(\frac{x}{5})^{3}$ i.e. $y=\frac{x^{3}}{125}$.

Further, the function is reflected over y-axis.

That is, the reflected function is $y=\frac{(-x)^{3}}{125}$ i.e. $y=\frac{-x^{3}}{125}$.

Hence, the required function is $y=\frac{-x^{3}}{125}$.