Question

What is the end behavior of the graph of the polynomial function f(x)

Answer 1

Answer:

f(x) approaches infinity as x approaches infinity

Explanation:

Given

$f(x) = 3x^6 + 30x^5+ 75x^4$

Required

The end behavior of the graph

 We have:

$f(x) = 3x^6 + 30x^5+ 75x^4$

The above expression implies that:

$f(x) = 3x^6 + 30x^5+ 75x^4$

The leading coefficient is 3 (3 is positive)

And the degree of the polynomial is 6 (6 is even)

When the leading coefficient is positive and the degree is even;  the end behavior of the function is:

$x \to \infty$

$f(x) \to \infty$