91Ó°ÊÓ

Graph each parabola. Give the vertex, axis of symmetry, domain, and range. \(f(x)=x^{2}+2 x-2\)

Use the tests for symmetry to decide whether the graph of each relation is symmetric with respect to the \(x\) -axis, the y-axis, or the origin. More than one of these symmetries, or none of them, may apply. $$ f(x)=\frac{-1}{x^{2}+9} $$

The snow depth in a particular location varies throughout the winter. In a typical winter, the snow depth in inches might be approximated by the following function. $$ f(x)=\left\\{\begin{array}{ll} 6.5 x & \text { if } 0 \leq x \leq 4 \\ -5.5 x+48 & \text { if } 4

In each problem, find the following. (a) A function \(R(x)\) that describes the total revenue received (b) The graph of the function from part (a) (c) The number of unsold seats that will produce the maximum revenue (d) The maximum revenue A charter flight charges a fare of \(\$ 200\) per person, plus \(\$ 4\) per person for each unsold seat on the plane. The plane holds 100 passengers. Let \(x\) represent the number of unsold seats. (Hint: To find \(R(x),\) multiply the number of people flying, \(100-x\), by the price per ticket, \(200+4 x\).)

Evaluate each expression. [-5]

A function \(f\) is an even function if \(f(-x)=f(x)\) for all \(x\) in the domain of \(f\). A function \(f\) is an odd function if \(f(-x)=-f(x)\) for all \(x\) in the domain of \(f\). To see how these ideas relate to symmetry, work in order. If a function is even, what do we know about its symmetry?

A function \(f\) is an even function if \(f(-x)=f(x)\) for all \(x\) in the domain of \(f\). A function \(f\) is an odd function if \(f(-x)=-f(x)\) for all \(x\) in the domain of \(f\). To see how these ideas relate to symmetry, work in order. If a function is odd, what do we know about its symmetry?

The tables give some selected ordered pairs for functions \(f\) and \(g\). $$\begin{array}{r|r}{x} & f(x) \\\\\hline-1 & 1 \\\\\hline 2 & -1 \\\\\hline 5 & 9\end{array}$$ $$\begin{array}{c|c}x & g(x) \\\\\hline 2 & -1 \\\\\hline 7 & 5 \\\\\hline 1 & 9 \\\\\hline 9 & 20\end{array}$$ Find each of the following. $$ (f \circ g)(7) $$