Question

How do you find the domain & range for `y=5cos(1/2)(x-(pi/4) +5`?

Answer 1

The domain of a sinusodial function is all the real numbers. The range, however, is determined by two things: the amplitude and the vertical displacement.

Explanation:

In function `f(x) = acosb(x - c) + d`, the amplitude is given by `|a|` and the vertical displacement is given by `d`.

Therefore, your function has a vertical displacement of `5` and an amplitude of `5`. A vertical displacement means you moved the graph up by `d` units from the x axis. The amplitude is the distance between the center line (`y = 5` in this case) and the maximum/minimum points of the function. Thus, the maximum points will be at `(x, 10) and (x, 0)`. The can be summarized as `"minimum in y"<= y <= "maximum in y "`, or in the case of this function, `0 <= y <= 10`.

In conclusion, the domain of `y = 5cos((1/2)(x - pi/4)) + 5` is `x="all the real numbers"` and the range is `0 <= y<= 10`.

Hopefully this helps!