Answer:
Answer a. between −2 & −1, between 3 & 4, and exactly at 1
Step-by-step explanation:
In order to guide your reasoning and analysis, start by evaluating the function at the points they are suggesting in the answers: -2, -1, 0, 1, 3, and 4.
Therefore, since this is a polynomial function, and all polynomial functions are continuous, we can infer that when the function goes from a negative value to a positive value at a near by point, its graph must be crossing the x-axis and therefore adopting the value zero at that crossing.
From the particular x-values at which we evaluated this function, we notide:
1) We have one of the zero values of the function at x=1 because f(1) is zero.
2) at x=-2, f(-2) gives a negative value. But when evaluated at x=-1, f(-1) renders a positive value. Therefore there must be a crossing of the x-axis (and therefore a zero) in between these two numbers.
3) At x=-1, f(-1) equals 2 (not zero)
4) For x-values in between -1 and 0, we cannot say anything, because both render positive values for f(x).
5) For x=3 f(3) renders a negative value, and at x=4 f(4) gives a positive value. Therefore we know that in between those values of x, the graph must be crossing the x-axis, rendering a zero for the function.
From all the study above, we conclude that answer a. is the correct one.
