Question

Determine the cubic function that is obtained from the parent function y = x^3 under a vertical stretch by a factor of ​5, a reflection across the​ x-axis, a vertical translation 1 unit down​, and a horizontal translation 7 units right .

Answer 1

Answer:

y = -5(x - 7)^3 - 1

Step-by-step explanation:

You kind of just plug in the numbers.

a vertical stretch by a factor of ​5: y = 5x^3

a reflection across the​ x-axis: y = -5x^3

a vertical translation 1 unit down: -5x^3 - 1

a horizontal translation 7 units right: -5(x - 7)^3 -1

Answer 2

Using translation concepts, it is found that the cubic function is given by:

$y = -5(x - 7)^3 - 1$

The parent function is given by:

$y = x^3$

A vertical stretch by a factor of 5 is the same as multiplying by 5, hence:

$y = 5x^3$

A reflection across the x-axis is the same as multiplying by -1, hence:

$y = -5x^3$

A vertical translation 1 unit down​ is the same as subtracting 1, hence:

$y = -5x^3 - 1$

A horizontal translation 7 units right means that $x \rightarrow x - 7$, hence:

$y = -5(x - 7)^3 - 1$

A similar problem is given at https://brainly.com/question/18405655