91Ó°ÊÓ

Determine whether the equation defines y as a function of \(x .\) \(y=\frac{3 x-1}{x+2}\)

Determine algebraically whether each function is even, odd, or neither. \(f(x)=x+|x|\)

Determine algebraically whether each function is even, odd, or neither. \(h(x)=\frac{x}{x^{2}-1}\)

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ g(x)=3|x+1|-3 $$

Find the sum function \((f+g)(x)\) if $$f(x)=\left\\{\begin{array}{ll}2 x+3 & \text { if } x<2 \\\x^{2}+5 x & \text { if } x \geq 2\end{array}\right.$$ and $$g(x)=\left\\{\begin{array}{ll}-4 x+1 & \text { if } x \leq 0 \\\x-7 & \text { if } x>0\end{array}\right.$$

Find the average rate of change of \(g(x)=x^{3}-4 x+7\) : (a) From -3 to -2 (b) From -1 to 1 (c) From 1 to 3

Find the domain of each function. \(M(t)=\sqrt[5]{\frac{t+1}{10}}\)

\(g(x)=x^{2}-2\) (a) Find the average rate of change from -2 to 1 . (b) Find an equation of the secant line containing \((-2, g(-2))\) and \((1, g(1))\).

Use a graphing utility. Consider the equation $$y=\left\\{\begin{array}{ll}1 & \text { if } x \text { is rational } \\\0 & \text { if } x \text { is irrational }\end{array}\right.$$ Is this a function? What is its domain? What is its range? What is its \(y\) -intercept, if any? What are its \(x\) -intercepts, if any? Is it even, odd, or neither? How would you describe its graph?

Suppose that the function \(y=f(x)\) is increasing on the interval [-1,5] (a) Over what interval is the graph of \(y=f(x+2)\) increasing? (b) Over what interval is the graph of \(y=f(x-5)\) increasing? (c) Is the graph of \(y=-f(x)\) increasing, decreasing, or neither on the interval [-1,5]\(?\) (d) Is the graph of \(y=f(-x)\) increasing, decreasing, or neither on the interval [-5,1]\(?\)