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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.

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nobillionaireNobley
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 [tex]y=x^3[/tex], a horizontal stretch by a factor of [tex]\frac{1}{5}[/tex] means that the x-value of the function is multiplied by [tex]\frac{1}{5}[/tex].

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

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, [tex]y=(\frac{1}{5}x)^3[/tex], refrection over the y-axis will result to the function [tex]y=(-\frac{1}{5}x)^3[/tex].

Therefore, the equation of the function that will result when the parent function, [tex]y=x^3[/tex], is horizontally stretched by a factor of [tex]\frac{1}{5}[/tex] and reflected over the y-axis is [tex]y=(-\frac{1}{5}x)^3[/tex].
hunchodraco1

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 .

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