Chapter 1

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. $$(f+g)(1)$$

Show that \(f\) and \(g\) are inverse functions algebraically. Use a graphing utility to graph \(f\) and \(g\) in the same viewing window. Describe the relationship between the graphs. $$f(x)=9-x^{2}, x \geq 0 ; \quad g(x)=\sqrt{9-x}$$

Determine whether the equation represents \(y\) as a function of \(x.\) $$y=\sqrt{x+5}$$

Determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=\frac{3}{2} x$$

Show that \(f\) and \(g\) are inverse functions algebraically. Use a graphing utility to graph \(f\) and \(g\) in the same viewing window. Describe the relationship between the graphs. $$f(x)=1-x^{3}, \quad g(x)=\sqrt[3]{1-x}$$

Determine whether the equation represents \(y\) as a function of \(x.\) $$2 x+3 y=4$$

Sketch the graph of the equation. \(y=2-x^{2}\)

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.) Point (7,-2) Slope \(m=\frac{1}{2}\)

Determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{2}-4 x$$

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. $$(f g)(4)$$

Show that \(f\) and \(g\) are inverse functions algebraically. Use a graphing utility to graph \(f\) and \(g\) in the same viewing window. Describe the relationship between the graphs. $$f(x)=\frac{1}{1+x}, x \geq 0 ; \quad g(x)=\frac{1-x}{x}, 0< x \leq 1$$

Determine whether the equation represents \(y\) as a function of \(x.\) $$x=-y+5$$

Sketch the graph of the equation. \(y=x^{3}-3\)

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.) Point (-1,-6) Slope \(m=-\frac{1}{3}\)

Determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{3}-3 x^{2}+2$$

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. $$(f / g)(-5)$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=-\frac{7}{2} x-3, \quad g(x)=-\frac{2 x+6}{7}$$

Sketch the graph of the equation. \(y=\sqrt{x-3}\)

$$f(x)=x^{3}-3 x^{2}+2$$

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. $$(0,-2), \quad m=3$$

Determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=\sqrt{x^{2}-1}$$

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. $$(f / g)(0)$$

Sketch the graph of the equation. \(y=\sqrt{1-x}\)

Determine whether the equation represents \(y\) as a function of \(x.\) $$x+y^{2}=3$$

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. $$(-3,6), \quad m=-3$$

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

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. $$(f-g)(t+1)$$

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

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

Sketch the graph of the equation. \(y=|x-2|\)

Determine whether the equation represents \(y\) as a function of \(x.\) $$y=|4-x|$$

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. $$(2,-3), \quad m=-\frac{1}{2}$$

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

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. $$(f+g)(t-3)$$

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

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

Sketch the graph of the equation. \(y=4-|x|\)

Determine whether the equation represents \(y\) as a function of \(x.\) $$|y|=3-2 x$$

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. $$(-2,-5), \quad m=\frac{3}{4}$$

Use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{2 / 3}$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=-\sqrt{x-8} ; \quad g(x)=8+x^{2}, \quad x \leq 0$$

(a) use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{2 / 3}$$

Sketch the graph of the equation. \(x=y^{2}-1\)

Determine whether the equation represents \(y\) as a function of \(x.\) $$x=-7$$

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. \((6,-1), \quad m\) 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. $$f(x)=-x^{3 / 4}$$

Show that \(f\) and \(g\) are inverse functions (a) algebraically, (b) graphically, and (c) numerically. $$f(x)=\sqrt[4]{3 x-10} ; \quad g(x)=\frac{x^{4}+10}{3}, \quad x \geq 0$$

(a) use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=-x^{3 / 4}$$

Sketch the graph of the equation. \(x=y^{2}+4\)

Determine whether the equation represents \(y\) as a function of \(x.\) $$y=8$$