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

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 .

Answer 2

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
`(1)/(5)` means that the x-value of the function is multiplied by
`(1)/(5)`.

Thus, after a horizontal stretch by a factor of
`(1)/(5)` of the parent function
`y=x^3`, we have
`y=((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=((1)/(5)x)^3`, refrection over the y-axis will result to the function
`y=(-(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
`(1)/(5)` and reflected over the y-axis is
`y=(-(1)/(5)x)^3`.