Chapter 1

1-48. Evaluate each expression without using a calculator. $$ \left(2^{2} \cdot 2\right)^{2} $$

Write each interval in set notation and graph it on the real line. $$ [0,6) $$

Evaluate each expression without using a calculator. $$ \left(5^{2} \cdot 4\right)^{2} $$

Write each interval in set notation and graph it on the real line. $$ (-3,5] $$

Evaluate each expression without using a calculator. $$ 2^{-4} $$

3-10 For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ f(x)=\frac{1}{x+4} ; \text { find } f(-3) $$

Write each interval in set notation and graph it on the real line. $$ (-\infty, 2] $$

Evaluate each expression without using a calculator. $$ 3^{-3} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ f(x)=\frac{1}{(x-1)^{2}} ; \text { find } f(-1) $$

Write each interval in set notation and graph it on the real line. $$ [7, \infty) $$

Evaluate each expression without using a calculator. $$ \left(\frac{1}{2}\right)^{-3} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ f(x)=\frac{x^{2}}{x-1} ; \text { find } f(-1) $$

Given the equation \(y=5 x-12,\) how will \(y\) change if \(x\) : a. Increases by 3 units? b. Decreases by 2 units?

Evaluate each expression without using a calculator. $$ \left(\frac{1}{3}\right)^{-2} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ f(x)=\frac{x^{2}}{x+2} ; \text { find } f(2) $$

Given the equation \(y=-2 x+7,\) how will \(y\) change if \(x\) : a. Increases by 5 units? b. Decreases by 4 units?

Evaluate each expression without using a calculator. $$ \left(\frac{5}{8}\right)^{-1} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ f(x)=\frac{12}{x(x+4)} ; \text { find } f(2) $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (2,3) \text { and }(4,-1) $$

Evaluate each expression without using a calculator. $$ \left(\frac{3}{4}\right)^{-1} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ f(x)=\frac{16}{x(x-4)} ; \text { find } f(-4) $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (3,-1) \text { and }(5,7) $$

Evaluate each expression without using a calculator. $$ 4^{-2} \cdot 2^{-1} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ g(x)=4^{x} ; \quad \text { find } g\left(-\frac{1}{2}\right) $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (-4,0) \text { and }(2,2) $$

Evaluate each expression without using a calculator. $$ \left(\frac{3}{2}\right)^{-3} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. [Hint: Use a graphing calculator. You may have to ignore some false lines on the graph. Graphing in "dot mode" will also eliminate false lines. $$ g(x)=8^{x} ; \quad \text { find } g\left(-\frac{1}{3}\right) $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (-1,4) \text { and }(5,1) $$

Evaluate each expression without using a calculator. $$ \left(\frac{3}{2}\right)^{-3} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. $$ f(x)=\sqrt{x-1} ; \text { find } f(10) $$

11-22. Solve each equation by factoring. [Hint for Exercises 19-22: First factor out a fractional power.] $$ x^{5}+2 x^{4}-3 x^{3}=0 $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (0,-1) \text { and }(4,-1) $$

Evaluate each expression without using a calculator. $$ \left(\frac{2}{3}\right)^{-3} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. $$ f(x)=\sqrt{x-4} ; \text { find } f(40) $$

Solve each equation by factoring. [Hint for: First factor out a fractional power.] $$ x^{6}-x^{5}-6 x^{4}=0 $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ \left(-2, \frac{1}{2}\right) \text { and }\left(5, \frac{1}{2}\right) $$

Evaluate each expression without using a calculator. $$ \left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-3} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. $$ h(z)=\frac{1}{z+4} ; \text { find } h(-5) $$

Solve each equation by factoring. [Hint for: First factor out a fractional power.] $$ 5 x^{3}-20 x=0 $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (2,-1) \text { and }(2,5) $$

Evaluate each expression without using a calculator. $$ \left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-2} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. $$ h(z)=\frac{1}{z+7} ; \text { find } h(-8) $$

Solve each equation by factoring. [Hint for: First factor out a fractional power.] $$ 2 x^{5}-50 x^{3}=0 $$

Find the slope (if it is defined) of the line determined by each pair of points. $$ (6,-4) \text { and }(6,-3) $$

Evaluate each expression without using a calculator. $$ \left[\left(\frac{2}{3}\right)^{-2}\right]^{-1} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. $$ h(x)=x^{1 / 4} ; \text { find } h(81) $$

Solve each equation by factoring. [Hint for: First factor out a fractional power.] $$ 2 x^{3}+18 x=12 x^{2} $$

For each equation, find the slope \(m\) and \(y\) -intercept \((0, b)\) (when they exist) and draw the graph. $$ y=3 x-4 $$.

Evaluate each expression without using a calculator. $$ \left[\left(\frac{2}{5}\right)^{-2}\right]^{-1} $$

For each function: a. Evaluate the given expression. b. Find the domain of the function. c. Find the range. $$ h(x)=x^{1 / 6} ; \text { find } h(64) $$