Question

Which of the following graphs could represent a quartic function?

Answer 1

Answer:

D. Graph D

Step-by-step explanation:

As we know,

Quartic function is a function of the form $f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e$, where a≠0.

That is, a quartic function is a polynomial of degree 4 called a quartic polynomial.

By the 'Fundamental Theorem of algebra', we have, 'An n-degree polynomial will have 'n' number of real roots'.

Thus, we get,

A quartic polynomial will have 4 real roots and so, a quartic function has 4 zeros.

Since, a quartic function has 4 zeros. Its graph will cut the y-axis at 4 points.

Moreover, when a graph touches the axis, it is known to be a repeated zero.

So, from the options, we get,

Option D represents a quartic function as one of its root is repeated and it cuts the the graph 4 times.