Question

Describe the end behavior of the following function: F(x)=x^5-x^3+x^2

Answer 1

Answer:The graph of the function starts high and ends low.

Step-by-step explanation:

Answer 2

Answer: The function has the end behavior $f(x)\rightarrow -\infty$  as $x\rightarrow -\infty$, $f(x)\rightarrow +\infty$  as $x\rightarrow +\infty$

Explanation:

Since,  The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.  And, if the function has  positive leading coefficient with odd degree then its end behavior is $f(x)\rightarrow -\infty$  as $x\rightarrow -\infty$, $f(x)\rightarrow +\infty$  as $x\rightarrow +\infty$

Here, The given function has positive leading coefficient with odd degree.

Therefore,  by the definition of end behavior of a function,

The function has the end behavior $f(x)\rightarrow -\infty$  as $x\rightarrow -\infty$

And, $f(x)\rightarrow +\infty$  as $x\rightarrow +\infty$