Question

2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
o g(x) = (x + 2)(x − 1)(x − 2)
o g(x) = (x + 3)(x + 2)(x − 3)
o g(x) = (x + 2)(x − 2)(x − 3)
o g(x) = (x + 5)(x + 2)(x − 5)
o g(x) = (x + 7)(x + 1)(x − 1)

Answer 1

Answer:

g(x) = (x + 2)(x − 1)(x − 2)

I picked the first one, because why not. :)

End behavior. This is a positive function; there are no negatives next to any of the xs. There are 3 xs, so it's a cubic; a positive cubic has a down-up end behavior.

Y-intercept. We can either graph this on the calculator/online or work it out algebraically. Multiply together the constants: +2 * -1 = -2, -2 * -2 = 4. So the y-intercept is at y = 4. (0,4). I've also attached the graph.

Zeros / x-intercept. This is really simple: set g(x) equal to 0, separate these three parenthesis (x+2) (x-1) and (x-2) into three equations by the Zero Product Property.

x+2 = 0

x = -2

x-1 = 0

x = 1

x-2 = 0

x = 2

So the function has three zeros at (-2,0) (1,0) and (2,0).