Chapter 1

Determine the slope \(m\) and \(y\) intercept \(b\) of the line with the given equation. Then sketch the line. \(y=-x\)

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ |y|=1 $$

Solve the inequality. $$ -1 \leq 2 x-3<4 $$

Sketch the graph of the function. $$ f(x)=x-[x] $$

Find the domain of the function. $$ f(x)=\sqrt{x(x-1)} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=x^{2}\) and \(g(x)=\sqrt{x}\)

Find the error. $$ \frac{e^{3}}{e^{\sqrt{2}} e^{\sqrt{2}}} \stackrel{?}{=} \frac{e^{3}}{e^{\sqrt{2}-\sqrt{2}}} \stackrel{?}{=} \frac{e^{3}}{e^{2}} \stackrel{?}{=} e $$

Determine the slope \(m\) and \(y\) intercept \(b\) of the line with the given equation. Then sketch the line. \(y=2 x-3\)

Sketch the graph of the function. Indicate any intercepts and symmetry, and determine whether the function is even, odd, or neither. $$ 2-\csc x $$

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ 4 x^{2}+4 y^{2}=9 $$

Solve the inequality. $$ -0.1<3 x+4<0.1 $$

Find the domain of the function. $$ f(t)=\sqrt{4-9 t^{2}} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=x^{6}\) and \(g(x)=x^{3 / 4}\)

Determine whether \(f\) is an even function, an odd function, or neither. $$ f(x)=e^{x} /\left(e^{2 x}+1\right) $$

Determine the slope \(m\) and \(y\) intercept \(b\) of the line with the given equation. Then sketch the line. \(y-1=2(x+3)\)

Sketch the graph of the function. Indicate any intercepts and symmetry, and determine whether the function is even, odd, or neither. $$ \sin 2 x $$

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ x=\sqrt{4-y^{2}} $$

Solve the inequality. $$ (x-1)(x+1 / 2) \geq 0 $$

Sketch the graph of the function. $$ f(x)=\left\\{\begin{array}{l} x \text { for } x<0 \\ 2 x \text { for } x \geq 0 \end{array}\right. $$

Find the domain of the function. $$ f(t)=\sqrt{3-\frac{1}{t^{2}}} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=\sqrt{x}\) and \(g(x)=x^{2}-5 x+6\)

Determine whether \(f\) is an even function, an odd function, or neither. $$ f(x)=\ln \left(e^{3 x}+1\right) $$

Determine the slope \(m\) and \(y\) intercept \(b\) of the line with the given equation. Then sketch the line. \(x-\frac{1}{2} y=2\)

Sketch the graph of the function. Indicate any intercepts and symmetry, and determine whether the function is even, odd, or neither. $$ \cos \frac{x-\pi}{2} $$

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ y=\sqrt{25-x^{2}} $$

Solve the inequality. $$ (x-1)(x-2)(x-3) \leq 0 $$

Sketch the graph of the function. $$ f(x)=\left\\{\begin{array}{l} x^{2} \text { for } x<0 \\ -x \text { for } x \geq 0 \end{array}\right. $$

Find the domain of the function. $$ f(t)=\frac{t}{\sqrt{t+5}} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=\frac{1}{x}\) and \(g(x)=x^{2}-3 x-10\)

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

Determine the slope \(m\) and \(y\) intercept \(b\) of the line with the given equation. Then sketch the line. \(2 x+y-4=0\)

Use the identities given in this section to compute the given value. $$ \sin \frac{7 \pi}{12}\left(\text { Hint }: \frac{7 \pi}{12}=\frac{\pi}{3}+\frac{\pi}{4}\right) $$

Solve the inequality. $$ x(x-2 / 3)(x+1 / 3)<0 $$

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ |y|=|3 x| $$

Sketch the graph of the function. The function \(f\) defined by $$ f(x)=\left\\{\begin{array}{ll} 3 & \text { for } x \neq 1 \\ 5 & \text { for } x=1 \end{array}\right. $$ A function whose graph resembles that of \(f\) can be called a "hiccup" function.

Find the domain of the function. $$ f(t)=\sqrt[3]{1-t^{2}} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=\frac{1}{x-1}\) and \(g(x)=\frac{1}{x+1}\)

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

Determine the slope \(m\) and \(y\) intercept \(b\) of the line with the given equation. Then sketch the line. \(\frac{2}{3} y-\frac{1}{3} x=2\)

Solve the inequality. $$ \frac{x}{(x-1)(x+2)}>0 $$

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ |2 y-3|=|x+4| $$

Sketch the graph of the function. The sign, or signum, function, defined by $$ f(x)=\left\\{\begin{aligned} -1 & \text { for } x<0 \\ 0 & \text { for } x=0 \\ 1 & \text { for } x>0 \end{aligned}\right. $$

Find the domain of the function. $$ g(x)=(x-6)^{1 / 4} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=\sqrt{x^{2}+3}\) and \(g(x)=\sqrt{x^{2}-4}\)

Sketch the graph of \(f\). $$ f(x)=\ln (x+1) $$

Decide which pairs of lines are parallel, which are perpendicular, and which are neither. For any pair that is not parallel, find the point of intersection. \(y-2 x=3\) and \(y+\frac{1}{2} x=-1\)

Solve the equation \(2 \sin ^{2} x+\sin x-1=0\).

Sketch the graph of the given equation with the help of a suitable translation. Show both the \(x\) and \(y\) axes and the \(X\) and \(Y\) axes. $$ (x-1)^{2}+(y-3)^{2}=4 $$

Solve the inequality. $$ \frac{(2 x-1)^{2}}{(x+1)(x+3)}>0 $$

Sketch the graph of the function. The diving board function, defined by $$ f(x)=\left\\{\begin{array}{ll} 0 & \text { for } x<0 \\ 1 & \text { for } x \geq 0 \end{array}\right. $$