I really need help on this question please.

Question

The function P(x) is mapped to I(x) by a dilation in the following graph.

Which answer gives the correct transformation of P(x) to get to I(x)?

A. I(x)=2P(x)

B. I(x)=P(2x)

C. I(x)=P(1/2x)

D. I(x)=1/2P(x)

Answer 1

We can see from the given graph that the y-intercepts of both I(x) and P(x) occur at the same point, which is y = 1. Based on this, we know that only the slope of I(x) is dilated from P(x). This eliminates answers A and D, since the dilations in these answers multiply the entire function and would change the intercept.

Now we can look at which slope dilation makes more sense. Answer B indicates that the dilation would be P(2x); in other words, the slope of I(x) would be twice that of P(x). Looking at the given graph, I(x) actually has a gentler slope, so we can eliminate answer B.

This leaves answer C, which indicates that the slope of I(x) is 1/2 that of P(x). Plotting this answer will verify that answer C is correct.