Chapter 3: Polynomial and Rational Functions

Properties of Real Numbers Rewrite the expression using the given property of real numbers.

Distributive property,$\mathbf{4}\mathbf{(}\mathbf{A}\mathbf{+}\mathbf{B}\mathbf{)}\mathbf{=}\mathbf{\_}\mathbf{\_}\mathbf{\_}\mathbf{\_}$

a. Using exponential notation, we can write the product$\mathbf{5}\mathbf{\cdot }\mathbf{5}\mathbf{\cdot }\mathbf{5}\mathbf{\cdot }\mathbf{5}\mathbf{\cdot }\mathbf{5}\mathbf{\cdot }\mathbf{5}$as ______.

b. In the expression${\mathbf{3}}^{\mathbf{4}}$the number 3is called the _______, and the number 4is called the ________.

To put the quadratic function $\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}\mathit{a}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathit{b}\mathit{x}\mathbf{+}\mathit{c}$in standard form, we complete the

.

Radicals and Exponents Write each radical expression using exponents, and each exponential expression using radicals.

$\sqrt[\mathbf{3}]{{\mathbf{7}}^{\mathbf{2}}}$

A quadratic function$\mathit{f}$ is given.

(a) Express$\mathit{f}$ in standard form.

(b) Find the vertex and$\mathit{x}$- and$\mathit{y}$- intercepts of$\mathit{f}$.

(c) Sketch a graph of$\mathit{f}$.

(d) Find the domain and range of$\mathit{f}$.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\mathit{x}\mathbf{-}\mathbf{1}$

A quadratic function$\mathit{f}$ is given.

(a) Express$\mathit{f}$ in standard form.

(b) Find the vertex and$\mathit{x}$- and$\mathit{y}$- intercepts of$\mathit{f}$.

(c) Sketch a graph of$\mathit{f}$.

(d) Find the domain and range of$\mathit{f}$.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{6}\mathit{x}$

Radicals and Exponents Write each radical expression using exponents, and each exponential expression using radicals.

${\mathbf{4}}^{\frac{\mathbf{2}}{\mathbf{3}}}$

A quadratic function$\mathit{f}$ is given.

(a) Express$\mathit{f}$ in standard form.

(b) Find the vertex and$\mathit{x}$- and$\mathit{y}$- intercepts of$\mathit{f}$.

(c) Sketch a graph of$\mathit{f}$.

(d) Find the domain and range of$\mathit{f}$.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{8}\mathit{x}$

Radicals and Exponents Write each radical expression using exponents, and each exponential expression using radicals.

${\mathbf{10}}^{\mathbf{-}\frac{\mathbf{3}}{\mathbf{2}}}$

A quadratic function$f$ is given.

(a) Express$f$ in standard form.

(b) Find the vertex and$x$- and$y$- intercepts of$f$.

(c) Sketch a graph of$f$.

(d) Find the domain and range of$f$.

$\mathit{f}\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{=}\mathbf{3}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{6}\mathit{x}$