If the function f(x) = acos[b(x + c)] + d has a range of [2, 6], the values of a and d are ___ and

Answer 1

The midline is the average of the high and low (2+6)/2 = 4. The midline is y = 4 (a vertical shift up 4 for the parent cosine function).

The amplitude is is the distance from the midline to either the high or low point (6-4) = 2.

y = 2 cos[b(x+c)] + 4

The values of b and c affect the period and cause a phase shift (horizontal shift).

desmos.com/calculator/lij7omdesf

Answer 2

d is the vertical shift and y = d is the midline of the graph; a is the amplitude

So, the graph varies between d - a and d + a.

a + d = 6

-a + d = 2

2d = 8 So, d = 4 and a = 2.