Chapter 1

Convert the following degree measures to radians (leave \(\pi\) in your answer). (a) \(30^{\circ}\) (b) \(45^{\circ}\) \(370^{\circ}(\mathrm{c})\) (c) \(-60^{\circ}\) (d) \(240^{\circ}\) (e) \(-370^{\circ}\) (f) \(10^{\circ}\)

In Problems \(1-4\), plot the given points in the coordinate plane and then find the distance between them. \((3,1),(1,1)\)

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ y=-x^{2}+1 $$

1\. For \(f(x)=x+3\) and \(g(x)=x^{2}\), find each value. (a) \((f+g)(2)\) (b) \((f \cdot g)(0)\) (c) \((g / f)(3)\) (d) \((f \circ g)(1)\) (e) \((g \circ f)(1)\) (f) \((g \circ f)(-8)\)

In Problems 1–6, sketch a graph of the given exponential function. $$ f(x)=3^{x} $$

For \(f(x)=1-x^{2}\), find each value. (a) \(f(1)\) (b) \(f(-2)\) (c) \(f(0)\) (d) \(f(k)\) (e) \(f(-5)\) (f) \(f\left(\frac{1}{4}\right)\) (h) \(f(1+h)-f(1)\) (g) \(f(1+h)\) (i) \(f(2+h)-f(2)\)

In Problems 1-10, find the exact value without using a calculator. $$ \arccos \left(\frac{\sqrt{2}}{2}\right) $$

1\. Show each of the following intervals on the real line. (a) \([-1,1]\) (b) \((-4,1]\) (c) \((-4,1)\) (d) \([1,4]\) (e) \([-1, \infty)\) (f) \((-\infty, 0]\)

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(4-2(8-11)+6\)

Convert the following radian measures to degrees. (a) \(\frac{7}{6} \pi\) (b) \(\frac{3}{4} \pi\) (c) \(-\frac{1}{3} \pi\) (d) \(\frac{4}{3} \pi\) (e) \(-\frac{35}{18} \pi\) (f) \(\frac{3}{18} \pi\)

In Problems \(1-4\), plot the given points in the coordinate plane and then find the distance between them. \((-3,5),(2,-2)\)

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ x=-y^{2}+1 $$

For \(f(x)=x^{2}+x\) and \(g(x)=2 /(x+3)\), find each value. (a) \((f-g)(2)\) (b) \((f / g)(1)\) (c) \(g^{2}(3)\) (d) \((f \circ g)(1)\) (e) \((g \circ f)(1)\) (f) \((g \circ g)(3)\)

In Problems 1–6, sketch a graph of the given exponential function. $$ f(x)=\frac{1}{3} 5^{x} $$

For \(F(x)=x^{3}+3 x\), find each value. (a) \(F(1)\) (b) \(F(\sqrt{2})\) (c) \(F\left(\frac{1}{4}\right)\) (e) \(F(1+h)-F(1)\) (d) \(F(1+h)\) (f) \(F(2+h)-F(2)\)

In Problems 1-10, find the exact value without using a calculator. $$ \arcsin \left(-\frac{\sqrt{3}}{2}\right) $$

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(3[2-4(7-12)]\)

Convert the following degree measures to radians \(\left(1^{\circ}=\pi / 180 \approx 1.7453 \times 10^{-2}\right.\) radian \() .\) (a) \(33.3^{\circ}\) (b) \(46^{\circ}\) (c) \(-66.6^{\circ}\) (d) \(240.11^{\circ}\) \(\begin{array}{ll}\text { (e) }-369^{\circ} & \text { (f) } 11^{\circ}\end{array}\)

In Problems \(1-4\), plot the given points in the coordinate plane and then find the distance between them. \((4,5),(5,-8)\)

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ x=-4 y^{2}-1 $$

For \(\Phi(u)=u^{3}+1\) and \(\Psi(v)=1 / v\), find each value. ( \(\Psi\) is the uppercase Greek letter psi.) (a) \((\Phi+\Psi)(t)\) (b) \((\Phi \circ \Psi)(r)\) (c) \((\Psi \circ \Phi)(r)\) (d) \(\Phi^{3}(z)\) (e) \((\Phi-\Psi)(5 t)\) (f) \(((\Phi-\Psi) \circ \Psi)(t)\)

In Problems 1–6, sketch a graph of the given exponential function. $$ f(x)=2^{2 x} $$

For \(G(y)=1 /(y-1)\), find each value. (a) \(G(0)\) (d) \(G\left(y^{2}\right)\) (b) \(G(0.999)\) (c) \(G(1.01)\) \(\left(y^{2}\right)(e) G(-x)\) (e) \(G(-x) \quad\) (f) \(G\left(\frac{1}{x^{2}}\right)\)

In Problems 1-10, find the exact value without using a calculator. $$ \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right) $$

Express the solution set of the given inequality in interval notation and sketch its graph. $$ x-7<2 x-5 $$

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(-4[5(-3+12-4)+2(13-7)]\)

Convert the following radian measures to degrees (1 radian \(=180 / \pi \approx 57.296\) degrees \()\). (a) \(3.141\) (b) \(6.28\) (c) \(5.00\) (d) \(0.001\) (e) \(-0.1\) (f) \(36.0\)

In Problems \(1-4\), plot the given points in the coordinate plane and then find the distance between them. \((-1,5),(6,3)\)

In Problems 1–6, sketch a graph of the given exponential function. $$ f(x)=2^{-3 x} $$

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ y=4 x^{2}-1 $$

If \(f(x)=\sqrt{x^{2}-1}\) and \(g(x)=2 / x\), find formulas for the following and state their domains. (a) \((f \cdot g)(x)\) (b) \(f^{4}(x)+g^{4}(x)\) (c) \((f \circ g)(x)\) (d) \((g \circ f)(x)\)

In Problems 1-10, find the exact value without using a calculator. $$ \sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right) $$

Express the solution set of the given inequality in interval notation and sketch its graph. $$ 3 x-5<4 x-6 $$

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(5[-1(7+12-16)+4]+2\)

Calculate (be sure that your calculator is in radian or degree mode as needed). (a) \(\frac{56.4 \tan 34.2^{\circ}}{\sin 34.1^{\circ}}\) (b) \(\frac{5.34 \tan 21.3^{\circ}}{\sin 3.1^{\circ}+\cot 23.5^{\circ}}\) (c) \(\tan 0.452\) (d) \(\sin (-0.361)\)

Show that the triangle whose vertices are \((5,3),(-2,4)\), and \((10,8)\) is isosceles.

In Problems 1–6, sketch a graph of the given exponential function. $$ f(x)=2^{\sqrt{x / 4}} $$

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ x^{2}+y=0 $$

If \(f(s)=\sqrt{s^{2}-4}\) and \(g(w)=|1+w|\), find formulas for \((f \circ g)(x)\) and \((g \circ f)(x)\).

In Problems 1-10, find the exact value without using a calculator. $$ \arctan (\sqrt{3}) $$

Express the solution set of the given inequality in interval notation and sketch its graph. $$ 7 x-2 \leq 9 x+3 $$

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(\frac{5}{7}-\frac{1}{13}\)

Calculate. (a) \(\frac{234.1 \sin 1.56}{\cos 0.34}\) (b) \(\sin ^{2} 2.51+\sqrt{\cos 0.51}\)

Show that the triangle whose vertices are \((2,-4),(4,0)\), and \((8,-2)\) is a right triangle.

In Problems 1–6, sketch a graph of the given exponential function. $$ f(x)=\frac{1}{2} 3^{-\sqrt{x}} $$

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ y=x^{2}-2 x $$

If \(g(x)=x^{2}+1\), find formulas for \(g^{3}(x)\) and \((g \circ g \circ g)(x)\).

For \(f(x)=\sqrt{x^{2}+9} /(x-\sqrt{3})\), find each value. (a) \(f(0.79)\) (b) \(f(12.26)\) (c) \(f(\sqrt{3})\)

In Problems 1-10, find the exact value without using a calculator. $$ \operatorname{arcsec}(2) $$

Express the solution set of the given inequality in interval notation and sketch its graph. $$ 5 x-3>6 x-4 $$