When 9x^2-100 is factored, it is equivalent to (3x-b)(3x+b). what is a value for b?

9x^2-100 is a perfect square

if we factor 9x^2-100= (3x-10)(3x+10)
therefore b=10

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.