Chapter 1

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(y=(6-x) \sqrt{x}\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$4 x-3 y-9=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$h(x)=(x-1) \sqrt{x}$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\frac{|x|}{x}$$ (a) \(f(9)\) (b) \(f(-9)\) (c) \(f(t)\)

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(y=\sqrt[3]{x-8}\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$x=-6$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$g(x)=x \sqrt{4-x}$$

Use a graphing utility to graph \(f, g,\) and \(f+g\) in the same viewing window. Which function contributes most to the magnitude of the sum when \(0 \leq x \leq 2 ?\) Which function contributes most to the magnitude of the sum when \(x>6 ?\) $$f(x)=x^{2}-\frac{1}{2}, \quad g(x)=-3 x^{2}-1$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=|x|+4$$ (a) \(f(5)\) (b) \(f(-5)\) (c) \(f(t)\)

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(y=\sqrt[3]{x+1}\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$y=12$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=x^{2}-4 x-5$$

Find \((\mathbf{a})\) \(\boldsymbol{f} \circ \boldsymbol{g},(\mathbf{b}) \boldsymbol{g} \circ \boldsymbol{f},\) and, if possible, \((\mathbf{c})(\boldsymbol{f} \circ \boldsymbol{g})(\mathbf{0}).\) $$f(x)=2 x^{2}, \quad g(x)=x+4$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\left\\{\begin{array}{ll}2 x+1, & x<0 \\ 2 x+2, & x \geq 0\end{array}\right.$$ (a) \(f(-1)\) (b) \(f(0)\) (c) \(f(2)\)

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(x^{2}-y=4 x-3\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$3 y+2=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=3 x^{2}-12 x$$

Find \((\mathbf{a})\) \(\boldsymbol{f} \circ \boldsymbol{g},(\mathbf{b}) \boldsymbol{g} \circ \boldsymbol{f},\) and, if possible, \((\mathbf{c})(\boldsymbol{f} \circ \boldsymbol{g})(\mathbf{0}).\) $$f(x)=\sqrt[3]{x-1}, \quad g(x)=x^{3}+1$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\left\\{\begin{array}{ll}2 x+5, & x \leq 0 \\ 2-x, & x>0\end{array}\right.$$ (a) \(f(-2)\) (b) \(f(0)\) (c) \(f(1)\)

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(2 y-x^{2}+8=2 x\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$2 x-5=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=x^{3}-3 x$$

Find \((\mathbf{a})\) \(\boldsymbol{f} \circ \boldsymbol{g},(\mathbf{b}) \boldsymbol{g} \circ \boldsymbol{f},\) and, if possible, \((\mathbf{c})(\boldsymbol{f} \circ \boldsymbol{g})(\mathbf{0}).\) $$f(x)=3 x+5, \quad g(x)=5-x$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\left\\{\begin{array}{ll}x^{2}+2, & x \leq 1 \\ 2 x^{2}+2, & x>1\end{array}\right.$$ (a) \(f(-2)\) (b) \(f(1)\) (c) \(f(2)\)

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(y-4 x=x^{2}(x-4)\)

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b). $$5 x-y+3=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=-x^{3}+3 x^{2}$$

Find \((\mathbf{a})\) \(\boldsymbol{f} \circ \boldsymbol{g},(\mathbf{b}) \boldsymbol{g} \circ \boldsymbol{f},\) and, if possible, \((\mathbf{c})(\boldsymbol{f} \circ \boldsymbol{g})(\mathbf{0}).\) $$f(x)=x^{3}, \quad g(x)=\frac{1}{x}$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\left\\{\begin{array}{ll}x^{2}-4, & x \leq 0 \\ 1-2 x^{2}, & x>0\end{array}\right.$$ (a) \(f(-2)\) (b) \(f(0)\) (c) \(f(1)\)

Using a Graphing Utility to Graph an Equation In Exercises \(31-44,\) use a graphing utility to graph the equation. Use a standard viewing window. Approximate any \(x\) - or \(y\) -intercepts of the graph. \(x^{3}+y=1\)

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b). $$2 x+3 y-9=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=3 x^{2}-6 x+1$$

Determine the domains of (a) \(f,\) (b) \(g\) and (c) \(f \circ g .\) Use a graphing utility to verify your results. $$f(x)=\sqrt{x-7}, \quad g(x)=4 x^{2}$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\left\\{\begin{array}{ll}x+2, & x<0 \\ 4, & 0 \leq x<2 \\ x^{2}+1, & x \geq 2\end{array}\right.$$ (a) \(f(-2)\) (b) \(f(0)\) (c) \(f(2)\)

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b). $$5 x-2=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=8 x-4 x^{2}$$

Determine the domains of (a) \(f,\) (b) \(g\) and (c) \(f \circ g .\) Use a graphing utility to verify your results. $$f(x)=\sqrt{x+3}, \quad g(x)=\frac{x}{2}$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\left\\{\begin{array}{ll}5-2 x, & x<0 \\ 5, & 0 \leq x<1 \\ 4 x+1, & x \geq 1\end{array}\right.$$ (a) \(f(-4)\) (b) \(f(0)\) (c) \(f(1)\)

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b). $$3 x+7=0$$

Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of \(g\) and \(h\) relative to the graph of \(f\).$$\begin{aligned}&f(x)=x^{3}-3 x^{2}\\\&g(x)=f(x+2)\\\&h(x)=\frac{1}{2} f(x)\end{aligned}$$

Use a graphing utility to graph the function and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $$h(x)=\frac{x^{2}}{x^{2}+1}$$

Determine the domains of (a) \(f,\) (b) \(g\) and (c) \(f \circ g .\) Use a graphing utility to verify your results. $$f(x)=x^{2}+1, \quad g(x)=\sqrt{x}$$

Assume that the domain of \(f\) is the set \(A=\\{-2,-1,0,1,2\\} .\) Determine the set of ordered pairs representing the function \(f.\) $$f(x)=(x-1)^{2}$$

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b). $$3 y+5=0$$

Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of \(g\) and \(h\) relative to the graph of \(f\).$$\begin{aligned}&f(x)=x^{3}-3 x^{2}+2\\\&g(x)=f(x-1)\\\&h(x)=f(3 x)\end{aligned}$$

Use a graphing utility to graph the function and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $$g(x)=\frac{4-x}{6 x^{2}}$$

Determine the domains of (a) \(f,\) (b) \(g\) and (c) \(f \circ g .\) Use a graphing utility to verify your results. $$f(x)=x^{1 / 4}, \quad g(x)=x^{4}$$

Sketch the graph of the function by hand. Then use a graphing utility to verify the graph. $$f(x)=[[x]]-3$$

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b). $$-11-4 y=0$$

Sketch the graph of the function by hand. Then use a graphing utility to verify the graph. $$f(x)=[\mid x-1] \mid-2$$