Question

question 1 of 10
which of the following graphs could represent a quartic function?
graphs a, b, c, d shown
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a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

A quartic function is a polynomial of degree 4 (highest exponent of \(x\) is 4). The end - behavior and the number of turning points are key. A quartic function can have up to 3 turning points.

• Graph B is a linear function (degree 1), so it can't be a quartic.
• Graph D is a constant function (degree 0), so it can't be a quartic.
• Graph C does not have the correct end - behavior or turning - point pattern for a quartic.
• Graph A has the potential to be a quartic function as it has multiple turning points and the end - behavior (as \(x\to\pm\infty\), the ends go in the same direction, which is consistent with a quartic with a positive leading coefficient) and a reasonable number of turning points.

Answer:

A. Graph A