Chapter 1

Find an equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible. \((-10,4), \quad m\) is undefined.

Use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x \sqrt{x+3}$$

Evaluate the indicated function for \(f(x)=x^{2}-1\) and \(g(x)=x-2\) algebraically. If possible, use a graphing utility to verify your answer. $$(f / g)(t-4)$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=2 x, \quad g(x)=\frac{x}{2}$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(t)=3 t+1$$ (a) \(f(2)\) (b) \(f(-4)\) (c) \(f(t+2)\)

(a) use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x \sqrt{x+3}$$

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. \(y=5-\frac{3}{2} x\)

Find an equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible. $$\left(-\frac{1}{2}, \frac{3}{2}\right), \quad m=0$$

Use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x \sqrt{3-x}$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=-3 x+5, \quad g(x)=-\frac{x-5}{3}$$

Evaluate the function at each specified value of the independent variable and simplify. $$g(y)=7-3 y$$ (a) \(g(0)\) (b) \(g\left(\frac{7}{3}\right)\) (c) \(g(s+5)\)

(a) use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x \sqrt{3-x}$$

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. \(y=\frac{2}{3} x-1\)

Find an equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible. $$(2.3,-8.5), \quad m=0$$

Use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=|x+1|+|x-1|$$

Use a graphing utility to graph the functions \(f, g,\) and \(h\) in the same viewing window. $$f(x)=\frac{1}{2} x, \quad g(x)=x-1, \quad h(x)=f(x)+g(x)$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=\frac{x-1}{x+5}, \quad g(x)=-\frac{5 x+1}{x-1}$$

(a) use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=|x+1|+|x-1|$$

Evaluate the function at each specified value of the independent variable and simplify. $$h(t)=t^{2}-2 t$$ (a) \(h(2)\) (b) \(h(1.5)\) (c) \(h(x-4)\)

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. \(y=|x+2|-3\)

Finance The median player salary for the New York Yankees was \(\$ 1.5\) million in 2007 and \(\$ 1.7\) million in 2013. Write a linear equation giving the median salary \(y\) in terms of the year \(x\). Then use the equation to predict the median salary in 2020 .

Use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=-|x+4|-|x+1|$$

Use a graphing utility to graph the functions \(f, g,\) and \(h\) in the same viewing window. $$f(x)=\frac{1}{3} x, \quad g(x)=-x+4, \quad h(x)=f(x)-g(x)$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=\frac{x+3}{x-2}, \quad g(x)=\frac{2 x+3}{x-1}$$

Evaluate the function at each specified value of the independent variable and simplify. $$V(r)=\frac{4}{3} \pi r^{3}$$ (a) \(V(3)\) (b) \(V\left(\frac{3}{2}\right)\) (c) \(V(2 r)\)

(a) use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=-|x+4|-|x+1|$$

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. \(y=-|x-3|+1\)

Finance The median player salary for the Dallas Cowboys was \(\$ 348,000\) in 2004 and \(\$ 555,000\) in 2013 . Write a linear equation giving the median salary \(y\) in terms of the year \(x .\) Then use the equation to predict the median salary in 2019 .

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

Use a graphing utility to graph the functions \(f, g,\) and \(h\) in the same viewing window. $$f(x)=x^{2}, \quad g(x)=-2 x+5, \quad h(x)=f(x) \cdot g(x)$$

Does the function have an inverse? Explain. Domain Range $$\begin{array}{c}1 \operatorname{can} \longrightarrow \$ 1 \\\6 \text { cans } \longrightarrow \$ 5 \\\12 \text { cans } \longrightarrow \$ 9 \\\24 \text { cans } \longrightarrow \$ 16\end{array}$$

Evaluate the function at each specified value of the independent variable and simplify. $$f(y)=3-\sqrt{y}$$ (a) \(f(4)\) (b) \(f(0.25)\) (c) \(f\left(4 x^{2}\right)\)

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. \(y=\frac{2 x}{x-1}\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$2 x-3 y=9$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$f(x)=3 x^{2}-2 x-5$$

Use a graphing utility to graph the functions \(f, g,\) and \(h\) in the same viewing window. $$f(x)=4-x^{2}, \quad g(x)=x, \quad h(x)=f(x) / g(x)$$

Does the function have an inverse? Explain. Domain Range \(1 / 2\) hour \(\longrightarrow \$ 40\) 1 hour 2 hours \(\longrightarrow . \$ 70\) 4 hours \(\longrightarrow \$ 120\)

Evaluate the function at each specified value of the independent variable and simplify. $$f(x)=\sqrt{x+8}+2$$ (a) \(f(-4)\) (b) \(f(8)\) (c) \(f(x-8)\)

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. \(y=\frac{10}{x^{2}+2}\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$3 x+4 y=1$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$y=-2 x^{3}-x^{2}+14 x$$

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 \(x>6 ?\) $$f(x)=3 x, \quad g(x)=-\frac{x^{3}}{10}$$

Does the function have an inverse? Explain. $$\\{(-3,6),(-1,5),(0,6)\\}$$

Evaluate the function at each specified value of the independent variable and simplify. $$q(x)=\frac{1}{x^{2}-9}$$ (a) \(q(-3)\) (b) \(q(2)\) (c) \(q(y+3)\)

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. \(y=x \sqrt{x+3}\)

Determine the slope and y-intercept (if possible) of the linear equation. Then describe its graph. $$2 x-5 y+10=0$$

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. $$y=x^{3}-6 x^{2}+15$$

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 \(x>6 ?\) $$f(x)=\frac{x}{2}, \quad g(x)=\sqrt{x}$$

Does the function have an inverse? Explain. $$\\{(2,4),(3,7),(7,2)\\}$$

Evaluate the function at each specified value of the independent variable and simplify. $$q(t)=\frac{2 t^{2}+3}{t^{2}}$$ (a) \(q(2)\) (b) \(q(0)\) (c) \(q(-x)\)