91Ó°ÊÓ

determine whether each function is even, odd, or neither. Then determine whether the function’s graph is symmetric with respect to the y-axis, the origin, or neither. $$ g(x)=x^{2}+x $$

In Exercises \(31-50,\) find \(f+g, f-g, f g,\) and \(\bar{g} .\) Determine the domain for each function. $$ f(x)=\sqrt{x}, g(x)=x-5 $$

determine whether each function is even, odd, or neither. Then determine whether the function’s graph is symmetric with respect to the y-axis, the origin, or neither. $$ g(x)=x^{2}-x $$

Graph the given functions, \(f\) and \(g,\) in the same rectangular coordinate system. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Once you have obtained your graphs, describe how the graph of g is related to the graph of \(f\) \(f(x)=x, g(x)=x-4\)

Give the slope and \(y\) -intercept of each line whose equation is given. Then graph the linear function. $$ y=3 x+2 $$

a. Find an equation for \(f^{-1}(x)\) b. Graph \(f\) and \(f^{-1}\) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of \(f\) and \(f^{-1}\). $$ f(x)=2 x-3 $$

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-2,0), r=6$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The graph of my function is not a straight line, so I cannot use slope to analyze its rates of change.

In Exercises \(31-50,\) find \(f+g, f-g, f g,\) and \(\bar{g} .\) Determine the domain for each function. $$ f(x)=2+\frac{1}{x}, g(x)=\frac{1}{x} $$

a. Find an equation for \(f^{-1}(x)\) b. Graph \(f\) and \(f^{-1}\) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of \(f\) and \(f^{-1}\). $$ f(x)=x^{2}-4, x \geq 0 $$