Question

question 4 of 25
which of the functions below could possibly have created this graph?
graph of a function
click here for long description
a. $f(x) = x^4 - x^3 - 3x^2 + 3$
b. $f(x) = -x^7 + 2x^4 + 6x$
c. $f(x) = -x^8 - x^3 - 3x^2 + 3$
d. $f(x) = x^5 + 13x^4 + 12x$

Explanation:

Step1: Check end behavior

The graph shows both ends going to +∞. For polynomials, even degree with positive leading coefficient has this end behavior.

Step2: Evaluate options

• A: Degree 4 (even), leading coefficient 1 (+) → matches end behavior.
• B: Degree7 (odd) → ends opposite → no.
• C: Degree8 (even), leading coefficient -1 (-) → ends to -∞ → no.
• D: Degree5 (odd) → ends opposite → no.

Answer:

A. \(F(x) = x^4 - x^3 - 3x^2 + 3\)