Chapter 1

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. $$ y^{2}=x \sqrt{1+x^{2}} $$

Sketch the graph of the function. $$ g(x)=|x+1| $$

Find the numerical value of the function at the given values of \(a\). $$ g(x)=4.5 x^{1 / 2}-x^{3 / 2} ; a=3,1.64 $$

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

Use a calculator to find the approximate value. $$ 2^{7 / 2} $$

Solve the inequality for \(x\) in \([0,2 \pi)\). $$ \cot x \geq \tan x $$

Find an equation of the line described. Then sketch the line. The line through \(\left(\frac{1}{2}, \frac{1}{2}\right)\) with slope \(-1\)

Write the union of the two intervals as a single interval. $$ (-3,2) \text { and }[1,4) $$

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. $$ \sqrt{x}+\sqrt{y}=1 $$

Sketch the graph of the function. $$ g(x)=|x-2| $$

Find the domain of the function. $$ f(x)=x^{3}-4 x+1 $$

Find the domains and rules of \(f+g, f g\), and \(f / g .\) $$ f(x)=\frac{2}{x-1} \text { and } g(x)=x-1 $$

Use a calculator to find the approximate value. $$ 10^{-5 / 3} $$

Solve the inequality for \(x\) in \([0,2 \pi)\). Decide whether each of the following functions is even or odd. a. \(\sin x\) b. \(\cos x\) c. \(\tan x\) d. \(\cot x\) e. \(\sec x\) f. \(\csc x\)

Find an equation of the line described. Then sketch the line. The line through \((0, \pi)\) with slope 0

Write the union of the two intervals as a single interval. $$ (-\infty, 0] \text { and }[0,3) $$

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. $$ y^{2}=\frac{x^{2}+1}{x^{2}-1} $$

Sketch the graph of the function. $$ f(t)=|t|+t $$

Find the domain of the function. $$ f(x)=x^{6}-\sqrt{2} x^{3}-\pi $$

Find the domains and rules of \(f+g, f g\), and \(f / g .\) \(f(x)=\frac{x+2}{x-3}\) and \(g(x)=\frac{x+3}{x^{2}-4}\)

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

Find an equation of the line described. Then sketch the line. The line with slope \(-1\) and \(y\) intercept 0

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ y=\frac{1}{3} x $$

Write the union of the two intervals as a single interval. $$ (1,3) \text { and }(2, \infty) $$

Sketch the graph of the function. $$ f(t)=|t|-t $$

Find the domain of the function. $$ k(x)=1+x^{3} \text { for }-2 \leq x \leq 8 $$

Find the domains and rules of \(f+g, f g\), and \(f / g .\) \(f(t)=t^{3 / 4}\) and \(g(t)=t^{2}+3\)

Calculate the logarithm by using \((11)\). $$ \log _{1 / 2} \frac{1}{3} $$

Sketch the graph of the function. Indicate any intercepts and symmetry, and determine whether the function is even, odd, or neither. $$ \sin \left(\frac{\pi}{4}-x\right) $$

Find an equation of the line described. Then sketch the line. The line with slope \(\frac{1}{2}\) and \(y\) intercept \(-1\)

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

Write the union of the two intervals as a single interval. $$ \left(-\infty, \frac{1}{2}\right] \text { and }(0, \infty) $$

Sketch the graph of the function. $$ f(t)=\frac{|t|}{t} $$

Find the domain of the function. $$ f(x)=2 x-3 x^{5} \text { for } x<4 $$

Find the domains and rules of \(f+g, f g\), and \(f / g .\) \(f(t)=\sqrt{1-t^{2}}\) and \(g(t)=\sqrt{2+t-t^{2}}\)

Calculate the logarithm by using \((11)\). $$ \log _{\pi} e $$

Sketch the graph of the function. Indicate any intercepts and symmetry, and determine whether the function is even, odd, or neither. $$ \tan \left(x+\frac{\pi}{2}\right) $$

Find an equation of the line described. Then sketch the line. The line with slope 3 and \(y\) intercept \(-3\)

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ y=x^{2}-3 $$

Solve the inequality. $$ -6 x-2>5 $$

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

Find the domain of the function. $$ f(x)=\sqrt{x+2} $$

Find the domain and rule of \(g \circ f\) and \(f \circ g\). \(f(x)=1-x\) and \(g(x)=2 x+5\)

Calculate the logarithm by using \((11)\). $$ \log _{\sqrt{2}} \sqrt{\pi} $$

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

Find an equation of the line described. Then sketch the line. The line with slope \(-2\) and \(y\) intercept \(\frac{5}{2}\)

Sketch the graph. List the intercepts and describe the symmetry (if any) of the graph. $$ |x|=2 $$

Solve the inequality. $$ 4-3 x \geq 7 $$

Find the domain of the function. $$ f(x)=\sqrt{2-3 x} $$

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