Question

What scale factor was used to transform f(x) into g(x)?

Answer 1

Answer:

The scale factor is k = 4.

Step-by-step explanation:

In the graph, we can see that g(x) is a dilation from f(x)

And a general vertical dilation of scale factor k is written as:

g(x) = k*f(x)

So here we want to find the value of k.

In the graph, we can see that:

f(1) = 1.5

f(3) = 0.5

Now, the values of g(x) in those x-values are:

g(1) = 6

g(3) = 2

And we must have:

g(1) = k*f(1)

g(3) = k*f(3)

we should get the same value of k in both equations, now let's replace the values of the functions:

For the ones evaluated in x = 1, we get:

6 = k*1.5

6/1.5 = k = 4

for the cases evaluated in x = 3, we get:

2 = k*0.5

2/0.5 = k = 4

In both cases we got the same value of k, so we can conclude that the scale factor from f(x) into g(x) is k = 4