91Ó°ÊÓ

Find the domain of the rational function.

$F\left(x\right)=\frac{3x\left(x-1\right)}{2x^2-5x-3}$

form a polynomial function f(x) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result.

Degree 4; zeros: 3 + 2i; 4 ; multiplicity 2

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 $f\left(x\right)$.

$f\left(x\right)=4x^6-64x^4+x^2-15;x+4$

In Problems 17, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor $f$over the real numbers.

$f\left(x\right)=4x^3+4x^2-7x+2$

Solve the inequality by using the graph of the function.

Solve $R\left(x\right)≤0$, where$R\left(x\right)=\frac{3x+3}{2x+4}$

In Problems 15–26, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell

why not.

$g\left(x\right)=\frac{1-x^2}{2}$

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

$R\left(x\right)=\frac{x^2}{x^2+x-6}$

Find the average rate of change of $f\left(x\right)=x^2+3x+1$from 1 to 2. Use this result to find the equation of the secant line containing$(1,f(1\left)\right),(2,(f\left(2\right))$

Find the domain of the rational function.