91Ó°ÊÓ

Express the solution set of the given inequality in interval notation and sketch its graph. $$ \frac{x+4}{x-3} \leq 0 $$

Sketch the graphs of the following on \([-\pi, 2 \pi]\). (a) \(y=\csc t\) (b) \(y=2 \cos t\) (c) \(y=\cos 3 t\) (d) \(y=\cos \left(t+\frac{\pi}{3}\right)\)

In Problems \(11-16\), find the inverse of the given function \(f\) and verify that \(f\left(f^{-1}(x)\right)=x\) for all \(x\) in the domain of \(f^{-1}\), and \(f^{-1}(f(x))=x\) for all \(x\) in the domain of \(f\). $$ f(x)=\log _{10}(3 x+2) $$

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. $$ 4(x-1)^{2}+y^{2}=36 $$

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. $$ x^{2}-4 x+3 y^{2}=-2 $$

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \((\sqrt{5}-\sqrt{3})^{2}\)

Sketch the graph of \(g(x)=|x+3|-4\) by first sketching \(h(x)=|x|\) and then translating.

In Problems 11-18, use a calculator to approximate each value. \(\tan ^{-1}(-60.11)\)

Express the solution set of the given inequality in interval notation and sketch its graph. $$ \frac{3 x-2}{x-1} \geq 0 $$

Determine the period, amplitude, and shifts (both horizontal and vertical) and draw a graph over the interval \(-5 \leq x \leq 5\) for the functions listed in Problems 16-23. $$ y=3 \cos \frac{x}{2} $$