Chapter 2.5, Problem 26AYU

In Problem 19-26, write the function whose graph is the graph of $y\text{ = }{x}^3$, but is:

Horizontally stretched by a factor of 4.

To determine

To find: The function which is horizontally stretched by a factor of 4 whose graph is the graph of $y=x^3$.

Answer to Problem 26AYU

$y=\frac{1}{4}{x}^3$

Explanation of Solution

Given:

$y=x^3$

Formula Used:

If the argument $x$ of a function $y=ƒ\left(x\right)$ is multiplied by a positive number $a$, the graph of the new function $y=ƒ\left(ax\right)$ is obtained by multiplying each $x\text{-coordinates}$ of $y=ƒ\left(x\right)$ by $\frac{1}{a}$.

The new graph is horizontally compressed if $a>1$.

Horizontally stretched if $0<a<1$.

Calculation:

To obtain the function which is horizontally stretched by a factor of 4.

Which means multiplying each $x\text{-coordinates}$ on the function $y=x^3$ by $\frac{1}{4}$.

We get, $y=\frac{1}{4}{x}^3$.