Question

The graph of y = cos x for -180 ≤ x ≤ 180 is shown. The graph (G) resulting from a transformation of y = cos x is also shown.

Answer 1

Answer: G(x) = cos(x) - 1

Step-by-step explanation:

We know that y = cos(x)

remember that cos(0) = 1.

Now, by looking at the image we can see that G(x) seems to be a vertical shift.

Remember that for a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

If N is positive, the shift is up

if N is negative, the shift is down.

In this case we can see that when x = 0, G(0) = 0.

And remember that cos(0) = 1, then G(x) is one unit below the graph of y = cos(x).

Then we can see that G(x) is a vertical shift of one unit downwards.

Then:

G(x) = cos(x) - 1