Find a and d for the function f(x) = a cos(x) + d such that the graph of f matches the figure.

Question

a =

d =

Answer 1

Note that the ticks on the y-axis are 1/2 apart.

The graph has a minimum of -9/2 and a maximum of -7/2. At 0, it is at a minimum. As cos has a max at 0, -cos has a min at 0.

a is the average of min and max, so (-9/2 + -7/2)/2 = -4. As it is 1 from min to max in the figure, and cos has a range of 2, d = 1/2.

a = -4

d = 1/2