Question

Let the graph of g be a vertical stretch by a factor of 3, followed by a translation 3 units down of the graph of f(x)=2x3+4x+2. Write a rule for g.

Answer 1

First we need to understand the transformation of the graph of f(x).

For a function f(x):

f(x-k) shifts graph to the right k units

f(x)+h shifts graph up h units

a*f(x) is a vertical stretch by a factor of a

-f(x) is a reflection over the x axis and f(-x) is a reflection over the y axis.

In the problem presented, we first do a vertical stretch by 3

f(x)-->3f(x)

Now we follow it up by a translation of 3 down

3f(x)-->3f(x)-3

We can now plug in the equation for f(x)

g(x) = 3(2x^3+4x+2)-3

And then simplify and combine liked terms

g(x)=6x^3+12x+3

I hope my answer helped please leave any questions in the comment.