Answer:
f(x) = 5x^3 -2
Step-by-step explanation:
We notice two things about the red graph, F(x). It has been shifted down and it is narrower.
Lets deal with the shifted down first. Looking at the point where it crosses the y axis on the graph of g(x) is 0
Looking at where it crosses the y axis for f(x) is -2
We have shifted the graph down 2
f(x) = g(x) + C
C > 0 moves it up
C < 0 moves it down
We will let c = -2
f(x) = g(x) -2
Now lets deal with the compression
f(x) = g(Cx)
C > 1 compresses it in the x-direction
0 < C < 1 stretches it
Since it got narrower, C > 1
our choices are 5 or negative 5 for the coefficient on x
Remember that the negative sign flips it across the x axis (reflections)
Since we do not have a reflection, we want positive 5
f(x) = 5x^3 -2
