F(x)=x+2, vertical stretch by factor of 5

We want to apply a vertical stretch to the function f(x) = x + 2.

We will find: g(x) = 5*x + 10

First, we should describe a vertical stretch, for a given function f(x) a vertical stretch of scale factor k is written as:

g(x) = k*f(x)

Then if the scale factor is k = 5 and the function is f(x) = x + 2 we get:

g(x) = 5*f(x) = 5*(x + 2) = 5*x + 10

g(x) = 5*x + 10

The image of the original (green) and stretched functions (blue) are shown below.

If you want to learn more, you can read:

link

Transformation from f(x) to g(x)

g(x)=a*f(x-h)+k

will

stretch vertically by a (if a>1, magnification, if 0<a<1 shrink)

translate to the right by h

translate upwards by k.

Since it is a pure stretch, h=0, k=0, and a=5

g(x)=5f(x)=5[(x-0)+2]+0=5x+10

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

the awnser is visionary