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

yes yes yes yes yes yes yes yes yes

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!