Question

which of the following correctly describes the end behavior of the polynomial function, f(x)=3x^4+2x^2-x

Answer 1

Answer:

$f(x)\rightarrow +\infty\text{ as }x\rightarrow -\infty$

$f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty$

Step-by-step explanation:

Given polynomial function is,

$f(x)=3x^4+2x^2-x$

Since, the end behavior of a polynomial is same as the end behavior of leading term,

Here, the leading term = $3x^4$

$\text{As }x\rightarrow -\infty$

The leading term is positive,

$\text{While, as }x\rightarrow +\infty$

The leading term is positive,

Hence, the end behavior of the given polynomial is,

$f(x)\rightarrow +\infty\text{ as }x\rightarrow -\infty$

$f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty$

⇒ In the graph of f(x), both ends will go upward.

Answer 2

Answer:both ends go down !

Step-by-step explanation: