Chapter 1

In Exercises 1-4, (a) write a formula for the function and (b) use the formula to find the indicated value of the function. the area A of a circle as a function of its diameter d; the area of a circle of diameter 4 in.

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {5 \pi / 8} & {2} & {? }\end{array}\)

In Exercises \(1-4,\) graph the function. State its domain and range. $$y=-2^{x}+3$$

In Exercises \(1-4,\) find the coordinate increments from \(A\) to \(B\). $$A(1,2), \quad B(-1,-1)$$

the height \(h\) of an equilateral triangle as a function of its side length s; the height of an equilateral triangle of side length 3 \(\mathrm{m}\)

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {175^{\circ}} & {?} & {10 }\end{array}\)

In Exercises \(1-4,\) graph the function. State its domain and range. $$y=e^{x}+3$$

In Exercises \(1-4,\) find the coordinate increments from \(A\) to \(B\) $$A(-3,2), \quad B(-1,-2)$$

the surface area \(S\) of a cube as a function of the length of the cube's edge \(e\) ; the surface area of a cube of edge length 5 \(\mathrm{ft}\)

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {?} & {14} & {7 }\end{array}\)

In Exercises \(1-4,\) graph the function. State its domain and range. $$y=3 \cdot e^{-x}-2$$

In Exercises \(1-4,\) find the coordinate increments from \(A\) to \(B\) $$A(-3,1), \quad B(-8,1)$$

the volume \(V\) of a sphere as a function of the sphere's radius \(r ;\) the volume of a sphere of radius 3 cm.

In Exercises \(1-4,\) the angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. \(\begin{array}{ll}{\text { Angle }} & {\text { Radius }} &{\text {Arc Length }} \\ {?} & {6} & {3 \pi / 2}\end{array}\)

In Exercises \(1-4,\) graph the function. State its domain and range. $$y=-2^{-x}-1$$

In Exercises \(1-4,\) find the coordinate increments from \(A\) to \(B\) $$A(0,4), \quad B(0,-2)$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=4-x^{2}$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=3 t, \quad y=9 t^{2}, \quad-\infty

In Exercises \(5-8,\) rewrite the exponential expression to have the indicated base. \(9^{2 x}, \quad\) base 3

In Exercises \(5-8,\) let \(L\) be the line determined by points \(A\) and \(B .\) \(\begin{array}{ll}{\text { (a) Plot } A \text { and } B .} & {\text { (b) Find the slope of } L} \\ {\text { (c) Draw the graph of } L .}\end{array}\) $$A(1,-2), \quad B(2,1)$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=x^{2}-9$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=-\sqrt{t}, \quad y=t, \quad t \geq 0$$

In Exercises \(5-8,\) rewrite the exponential expression to have the indicated base. \(16^{3 x}, \quad\) base 2

In Exercises \(5-8,\) let \(L\) be the line determined by points \(A\) and \(B .\) \(\begin{array}{ll}{\text { (a) Plot } A \text { and } B .} & {\text { (b) Find the slope of } L} \\ {\text { (c) Draw the graph of } L .}\end{array}\) $$A(-2,-1), \quad B(1,-2)$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? \(x=t, \quad y=\sqrt{t}, \quad t \geq 0\)

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=2+\sqrt{x-1}$$

In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=\frac{3}{x-2}-1$$

In Exercises \(5-8,\) rewrite the exponential expression to have the indicated base. \((1 / 8)^{2 x}, \quad\) base 2

In Exercises \(5-8,\) let \(L\) be the line determined by points \(A\) and \(B .\) \(\begin{array}{ll}{\text { (a) Plot } A \text { and } B .} & {\text { (b) Find the slope of } L} \\ {\text { (c) Draw the graph of } L .}\end{array}\) $$A(2,3), \quad B(-1,3)$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=-\sqrt{-x}$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=\left(\sec ^{2} t\right)-1, \quad y=\tan t, \quad-\pi / 2

In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=x^{2}+5 x$$

In Exercises \(5-8,\) rewrite the exponential expression to have the indicated base. \((1 / 27)^{x}, \quad\) base 3

In Exercises \(5-8,\) let \(L\) be the line determined by points \(A\) and \(B .\) \(\begin{array}{ll}{\text { (a) Plot } A \text { and } B .} & {\text { (b) Find the slope of } L} \\ {\text { (c) Draw the graph of } L .}\end{array}\) $$A(1,2), \quad B(1,-3)$$

In Exercises 9 and \(10,\) find all the trigonometric values of \(\theta\) with the given conditions. $$\cos \theta=-\frac{15}{17}, \quad \sin \theta>0$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=\frac{1}{x-2}$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=\cos t, \quad y=\sin t, \quad 0 \leq t \leq \pi$$

In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=x^{3}-4 x+6$$

In Exercises \(9-12,\) use a graph to find the zeros of the function. $$f(x)=2^{x}-5$$

In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(3,2)$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=\sqrt[4]{-x}$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=\sin (2 \pi t), \quad y=\cos (2 \pi t), \quad 0 \leq t \leq 1$$

In Exercises \(7-12,\) determine whether the function has an inverse function. $$y=x^{3}+x$$

In Exercises 9 and \(10,\) find all the trigonometric values of \(\theta\) with the given conditions. $$\tan \theta=-1, \quad \sin \theta<0$$

In Exercises \(9-12,\) use a graph to find the zeros of the function. $$f(x)=e^{x}-4$$

In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(-1,4 / 3)$$

In Exercises \(11-14,\) determine (a) the period, (b) the domain, (c) the range, and (d) draw the graph of the function. $$y=3 \csc (3 x+\pi)-2$$

In Exercises 5-12, (a) identify the domain and range and (b) sketch the graph of the function. $$y=1+\frac{1}{x}$$

In Exercises \(5-22,\) a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? $$x=\cos (\pi-t), \quad y=\sin (\pi-t), \quad 0 \leq t \leq \pi$$

In Exercise \(9-12,\) write an equation for (a) the vertical line and (b) the horizontal line through the point \(P .\) $$P(0,-\sqrt{2})$$