91Ó°ÊÓ

Using Intercepts and Symmetry to Sketch a Graph In Exercises \(41-56,\) find any intercepts and test for symmetry. Then sketch the graph of the equation. \(x=y^{4}-16\)

Period In Exercises \(49-52,\) find the period of the function. $$y=7 \tan 2 \pi x$$

Finding an Equation of a Line In Exercises \(43-50,\) find an equation of the line that passes through the points. Then sketch the line. \((2,5),(2,7)\)

Period In Exercises \(49-52,\) find the period of the function. $$y=\sec 5 x$$

Using Intercepts and Symmetry to Sketch a Graph In Exercises \(41-56,\) find any intercepts and test for symmetry. Then sketch the graph of the equation. \(y=\frac{8}{x}\)

Writing an Equation Write an equation for the line that passes through the points \((0, b)\) and \((3,1)\) .

Using Intercepts Show that the line with intercepts \((a, 0)\) and \((0, b)\) has the following equation. $$\frac{x}{a}+\frac{y}{b}=1, \quad a \neq 0, b \neq 0$$

Period In Exercises \(49-52,\) find the period of the function. $$y=\csc 4 x$$

Using Intercepts and Symmetry to Sketch a Graph In Exercises \(41-56,\) find any intercepts and test for symmetry. Then sketch the graph of the equation. \(y=\frac{10}{x^{2}+1}\)

Writing In Exercises 53 and \(54,\) use a graphing utility to graph each function \(f\) in the same viewing window for \(c=-2\) , \(c=-1, c=1,\) and \(c=2 .\) Give a written description of the change in the graph caused by changing \(c .\) $$\begin{array}{l}{\text { (a) } f(x)=c \sin x} \\ {\text { (b) } f(x)=\cos (c x)} \\ {\text { (c) } f(x)=\cos (\pi x-c)}\end{array}$$