Chapter 1

$$ \ln e^{3} $$

Draw a set of coordinate axes and plot the following points. a. \((2,1)\) b. \((-1,3)\) c. \((4,0)\) d. \(\left(0,-\frac{3}{2}\right)\) e. \((1,-1)\) f. \((-2,-2)\) g. \((0,0)\) h. \(\left(3,-\frac{1}{3}\right)\)

Sketch the graph of the function. $$ f(x)=\frac{1}{2} x+1 $$

Convert the following degree measures to radians. a. \(210^{\circ}\) b. \(-405^{\circ}\) c. \(1^{\circ}\)

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ x=3 y^{2}-2 $$

Determine whether \(ab\). \(a=\frac{4}{9}, b=\frac{7}{16}\)

Let \(f(x)=2 x^{2}+x-4\) and \(g(x)=3-x^{2} .\) Find the specified values. $$ (f+g)(-1) $$

$$ \ln \sqrt{e} $$

Let \((a, b)\) be any point in the second quadrant. Describe the locations of the following points. a. \((-a, b)\) b. \((a,-b)\) c. \((-a,-b)\)

Sketch the graph of the function. $$ f(x)=1-3 x \text { for }-1 \leq x \leq 2 $$

Convert the following radian measures to degrees. a. \(\frac{\pi}{8}\) b. \(-\frac{3 \pi}{10}\) c. \(\frac{13 \pi}{6}\)

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ 4 x^{2}+y^{2}=12 $$

Find the numerical value of the function at the given values of \(a\). $$ f(x)=2 x^{2}-3 ; a=1,-2 $$

Let \(f(x)=2 x^{2}+x-4\) and \(g(x)=3-x^{2} .\) Find the specified values. $$ (f-g)(2) $$

Determine whether \(ab\). \(a=-\frac{1}{7}, b=-0.142857\)

$$ e^{\ln 3 x} $$

Determine the distance between the given points. \((3,0)\) and \((-2,0)\)

Find the following values. a. \(\sin \frac{11 \pi}{6}\) b. \(\sin \left(-\frac{2 \pi}{3}\right)\) c. \(\cos \frac{5 \pi}{4}\) d. \(\cos \left(-\frac{7 \pi}{6}\right)\) e. \(\tan \frac{4 \pi}{3}\) f. \(\tan \left(-\frac{\pi}{4}\right)\) g. \(\cot \frac{\pi}{6}\) h. \(\cot \left(-\frac{17 \pi}{3}\right) \quad \mathbf{i} . \sec 3 \pi\) j. \(\sec \left(-\frac{\pi}{3}\right)\) k. \(\csc \frac{\pi}{2}\) L. \(\csc \left(-\frac{5 \pi}{3}\right)\)

Sketch the graph of the function. $$ f(x)=x^{2} $$

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ x^{2}-y^{2}=1 $$

Find the numerical value of the function at the given values of \(a\). $$ f(x)=1-x+x^{3} ; a=0,-1 $$

Determine whether \(ab\). $$ a=\pi^{2}, b=9.8 $$

Let \(f(x)=2 x^{2}+x-4\) and \(g(x)=3-x^{2} .\) Find the specified values. $$ (f g)\left(\frac{1}{2}\right) $$

$$ e^{-4 \ln x} $$

Determine the distance between the given points. \((0,0)\) and \((3,4)\)

For each of the following intervals, state which of the six trigonometric functions have positive values throughout the interval. a. \(\left(0, \frac{\pi}{2}\right)\) b. \(\left(\frac{\pi}{2}, \pi\right)\) c. \(\left(\pi, \frac{3 \pi}{2}\right)\) d. \(\left(\frac{3 \pi}{2}, 2 \pi\right)\) e. \((3 \pi, 4 \pi)\)

Sketch the graph of the function. $$ f(x)=x^{2}+2 $$

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ x^{2}=y^{15}-y^{9} $$

Find the numerical value of the function at the given values of \(a\). $$ f(x)=1 / x ; a=2, \frac{1}{2} $$

Determine whether \(ab\). $$ a=(3.2)^{2}, b=10 $$

Let \(f(x)=2 x^{2}+x-4\) and \(g(x)=3-x^{2} .\) Find the specified values. $$ (f / g)(-3) $$

$$ \ln \left(e^{\ln e}\right) $$

Determine the distance between the given points. \((2,1)\) and \((6,-3)\)

Sketch the graph of the function. $$ f(x)=x^{2}-1 \text { for }-2 \leq x \leq 2 $$

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ x^{4}=3 y^{3} $$

Find the numerical value of the function at the given values of \(a\). $$ g(x)=1 /\left(2 x^{2}\right) ; a=\sqrt{2} $$

Use the fact that \((\sqrt{2})^{2}=2\) to determine whether \(\sqrt{2}<\) \(1.41, \sqrt{2}=1.41\), or \(\sqrt{2}>1.41\)

Let \(f(x)=2 x^{2}+x-4\) and \(g(x)=3-x^{2} .\) Find the specified values. $$ f(g(1)) $$

$$ \ln |\ln (1 / e)| $$

Determine the distance between the given points. \((-1,-3)\) and \((-2,2)\)

Find the values of the remaining four trigonometric functions under the given conditions. $$ \cos x=\frac{1}{3} \text { and } \tan x=2 \sqrt{2} $$

Sketch the graph of the function. $$ f(x)=x^{3} $$

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ x^{4}=3 y^{3}+4 $$

Find the numerical value of the function at the given values of \(a\). $$ g(x)=\sqrt{x} ; a=4, \frac{1}{25} $$

Use the fact that \((\sqrt{11})^{2}=11\) to determine whether \(\sqrt{11}<3.3, \sqrt{11}=3.3\), or \(\sqrt{11}>3.3\)

Let \(f(x)=2 x^{2}+x-4\) and \(g(x)=3-x^{2} .\) Find the specified values. $$ g(f(0)) $$

Solve the equation for \(x\) in \([0,2 \pi)\). $$ \sin x=-\frac{1}{5} $$

Determine the distance between the given points. \((6,5)\) and \((-3,-4)\)

Sketch the graph of the function. $$ y=\sqrt{x} $$

Determine all intercepts of the graph of the equation. Then decide whether the graph is symmetric with respect to the \(x\) axis, the \(y\) axis, or the origin. $$ x^{2} y^{4}-2 x^{4}=1 $$