91Ó°ÊÓ

Determine whether the function is one-to-one. $$f(x)=\frac{1}{x^{2}}$$

Evaluate the function at the indicated values. $$\begin{aligned}&g(x)=\frac{1-x}{1+x}\\\&g(2), g(-2), g\left(\frac{1}{2}\right), g(a), g(a-1), g(-1)\end{aligned}$$

Sketch the graph of the function by first making a table of values. \(H(x)=|2 x|\)

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x\)- and \(y\)-intercept(s). (c) Sketch its graph. $$f(x)=2 x^{2}-20 x+57$$

Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$f(x)=x^{2}, \quad g(x)=\frac{1}{3} x^{3}$$

A quadratic function is given. (a) Express the quadratic function in standard form. (b) Find its vertex and its \(x\)- and \(y\)-intercept(s). (c) Sketch its graph. $$f(x)=2 x^{2}+x-6$$

In these exercises you are asked to find a function that models a real-life situation. Use the guidelines for modeling described in the text to help you. Perimeter \(\quad\) A right triangle has one leg twice as long as the other. Find a function that models its perimeter \(P\) in terms of the length \(x\) of the shorter leg.

Draw the graphs of \(f, g,\) and \(f+g\) on a common screen to illustrate graphical addition. $$f(x)=\sqrt[4]{1-x}, \quad g(x)=\sqrt{1-\frac{x^{2}}{9}}$$

Determine whether the function is one-to-one. $$f(x)=\frac{1}{x}$$

Sketch the graph of the function by first making a table of values. \(H(x)=|x+1|\)