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
