Question

State the y- intercept

State the zeros of the function
State which graph below is the graph of P(x)

Answer 1

End behavior like that shown in option A.

y-intercept: y = -3

zeroes at: x = -1, x = -3, and x = 2

GRAPH C

Explanation:

The end behavior of the function can be studied from it polynomial form, and i particular from its leading term:
`(1)/(2) x^3`. since this is a cubic polynomial with positive leading coefficient, the end behavior would be that of
`x^3`, which is similar to the sketch shown in option A.

The y-intercept is also easier to find by using the polynomial form of the function, since it is easy to find where the graph intercepts the y-axis by evaluating it at x=0, which cancels all non-constant terms of the polynomial and leaves as with y = -3

For the zeroes of the function, it is simpler to study its "binomial factor" form, looking for which values of the variable "x" make zero each of the binomial factors. Such study gives us that:

x = -1 is a zero because it cancels out the factor (x+1)

x = -3 is a zero because it cancels out the factor (x+3)

x = 2 is a zero because it cancels out the factor (x-2)

Therefore, following the information found above, we conclude that Graph C is the representation of the graph of our polynomial.