1 Suppose f(x) = x2 - x - 12, g(x) = x + 3, and h(x) = 6x - 1. Which of the following function operations are
three that apply.
A (g x h)(x) = 6x2 + 17x-3
B (n + 1)(x) = x2 + 5x - 13
C (f = g)(x) = x - 4
D (f - h)(x) = x2 - 7x-13
E (g- h)(x) = 5x - 4
о

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.