The graph of a cosine function is drawn. One full cycle goes from x=0 to x=2 and the low point on that cycle is (1,-5). Which of the following functions could have this graph?

Question

The graph of a cosine function is drawn. One full cycle goes from x=0 to x=2 and the low point on that cycle is (1,-5). Which of the following functions could have this graph?

Answer 1

One possible function that could have this graph is:

$f(x) = -5\cos\left(\frac{2\pi}{2}x\right) + 1$

This function has an amplitude of 5 and a period of 2, which matches the given information about the graph. The vertical shift of 1 matches the low point being at (1,-5).