Question

Identify the equation of the parent function, y+x^3, that is horizontally stretched by a factor of 1/5 and reflected over the y-axis.

Answer 1

A horizontal stretching is the stretching of the graph away from the y-axis. When a function is horizontally stretched by a factor, k, the x-value of the function is multiplied by the factor k.

Thus, given the parent function $y=x^3$, a horizontal stretch by a factor of $\frac{1}{5}$ means that the x-value of the function is multiplied by $\frac{1}{5}$.

Thus, after a horizontal stretch by a factor of $\frac{1}{5}$ of the parent function $y=x^3$, we have $y=(\frac{1}{5}x)^3$.

Refrection of the graph of a function over the y-axis results from adding minus to the x-term of the function.

Thus given the function, $y=(\frac{1}{5}x)^3$, refrection over the y-axis will result to the function $y=(-\frac{1}{5}x)^3$.

Therefore, the equation of the function that will result when the parent function, $y=x^3$, is horizontally stretched by a factor of $\frac{1}{5}$ and reflected over the y-axis is $y=(-\frac{1}{5}x)^3$.

Answer 2

Answer:

Step-by-step A horizontal stretching is the stretching of the graph away from the y-axis. When a function is horizontally stretched by a factor, k, the x-value of the function is multiplied by the factor k.

Thus, given the parent function , a horizontal stretch by a factor of  means that the x-value of the function is multiplied by .

Thus, after a horizontal stretch by a factor of  of the parent function , we have .

Refrection of the graph of a function over the y-axis results from adding minus to the x-term of the function.

Thus given the function, , refrection over the y-axis will result to the function .

Therefore, the equation of the function that will result when the parent function, , is horizontally stretched by a factor of  and reflected over the y-axis is .