91Ó°ÊÓ

If $f\left(x\right)=-2x^5+x^3-5x^2+7$, then $\underset{x→-∞}{\lim }f\left(x\right)=\_\_\_\_\_\_\_\_$and$\underset{x→∞}{\lim }f\left(x\right)=\_\_\_\_\_\_\_\_$.

Solve the inequality by using the graph of the function.

Solve $f\left(x\right)≤0$, where

$f\left(x\right)=-2(x+2)(x-2{)}^3$

In Problems $7-44$, follow Steps $1$through $7$on page $228$to analyze the graph of each function.

$P\left(x\right)=\frac{x^4+x^2+1}{x^2-1}$

Is the following the graph of a function? Why or why not?

Explain what the notation$\underset{x→∞}{\lim }f\left(x\right)=-∞$means

Solve the inequality by using the graph of the function.

Solve $f\left(x\right)<0$, where

role="math" localid="1646231564659" $f\left(x\right)=-\frac{1}{2}(x+4)(x-1{)}^3$

For the function $f\left(x\right)=x^2+5x-2$

Find

$$\begin{gathered} a)f(3\left) \\ b\right)f(-x) \\ c)-f(x\left) \\ d\right)f\left(3x\right) \\ e)\frac{f(x+h)-f\left(x\right)}{h} \end{gathered}$$

Use the Remainder Theorem to find the remainder when $f\left(x\right)$is divided by $x-c$. Then use the Factor Theorem to determine whether $x-c$is a factor of $f\left(x\right)$.

$f\left(x\right)=4x^4-15x^2-4;x-2$

Find the value of $f\left(x\right)=12x^6-8x^4+1$ at $x=4$.

Find the remaining zeros of $f\left(x\right)$with real coefficients and given information.

The degree is 4 and zeros are$2-i,-i$