Chapter 1

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

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) \((g \circ f)(-8)\)

find the exact value without using a calculator. $$ \arccos \left(\frac{\sqrt{2}}{2}\right) $$

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

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) \(f\left(\frac{1}{4}\right)\) (g) \(f(1+h)\) (h) \(f(1+h)-f(1)\) (i) \(f(2+h)-f(2)\)

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

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

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) \((-\infty, 0]\)

In Problems 1-16, simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. $$ 4-2(8-11)+6 $$

Sketch a graph of the given exponential function. $$ f(x)=\frac{1}{3} 5^{x} $$

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) \((g \circ g)(3)\)

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

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) \(\frac{3}{18} \pi\)

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

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

Plot the given points in the coordinate plane and then find the distance between them. $$ (-3,5),(2,-2) $$

In Problems , simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. $$ 3[2-4(7-12)] $$

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

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) \(\left(\begin{array}{lll}\Phi & \circ & \Psi\end{array}\right)(r)\) (c) \((\Psi \circ \Phi)(r)\) (d) \(\Phi^{3}(z)\) (e) \((\Phi-\Psi)(5 t)\) (f) \(((\Phi-\Psi) \circ \Psi)(t)\)

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

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) \(240.11^{\circ}\) (e) \(-369^{\circ}\) (f) \(11^{\circ}\)

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

Plot the given points in the coordinate plane and then find the distance between them. $$ (4,5),(5,-8) $$

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

In Problems , simplify as much as possible. Be sure to remove all parentheses and reduce all fractions.$$ -4[5(-3+12-4)+2(13-7)] $$

Sketch a graph of the given exponential function. $$ f(x)=2^{-3 x} $$

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) \((g \circ f)(x)\)

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

For \(\Phi(u)=\frac{u+u^{2}}{\sqrt{u}}\), find each value. ( \(\Phi\) is the uppercase Greek letter phi.) (a) \(\Phi(1)\) (b) \(\Phi(-t)\) (c) \(\Phi\left(\frac{1}{2}\right)\) (d) \(\Phi(u+1)\) (e) \(\Phi\left(x^{2}\right)\) (f) \(\Phi\left(x^{2}+x\right)\)

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

Plot the given points in the coordinate plane and then find the distance between them. $$ (-1,5),(6,3) $$

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

In Problems , simplify as much as possible. Be sure to remove all parentheses and reduce all fractions.$$ 5[-1(7+12-16)+4]+2 $$

Sketch a graph of the given exponential function. $$ f(x)=2^{\sqrt{x / 4}} $$

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

find the exact value without using a calculator. $$ \arctan (\sqrt{3}) $$

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) \(\sin (-0.361)\)

For $$ f(x)=\frac{1}{\sqrt{x-3}} $$ find each value. (a) \(f(0.25)\) (b) \(f(\pi)\) (c) \(f(3+\sqrt{2})\)

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

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

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. $$ \frac{5}{7}-\frac{1}{13} $$

Sketch a graph of the given exponential function. $$ f(x)=\frac{1}{2} 3^{-\sqrt{x}} $$

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

find the exact value without using a calculator. $$ \operatorname{arcsec}(2) $$

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

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

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

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

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