91Ó°ÊÓ

In Exercises \(41-52,\) give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$x^{2}+y^{2}=49$$

Find \(f+g, f-g,\) fg, and \(\frac{f}{8} .\) Determine the domain for each function. $$f(x)=\frac{5 x+1}{x^{2}-9}, g(x)=\frac{4 x-2}{x^{2}-9}$$

In Exercises \(41-52,\) give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$(x-3)^{2}+(y-1)^{2}=36$$

give the slope and y-intercept of each line whose equation is given. Then graph the linear function. $$f(x)=\frac{3}{4} x-2$$

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

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 \(f^{-1}\). $$f(x)=(x-1)^{2}, x \leq 1$$

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 \(f\). $$f(x)=x^{2}, g(x)=x^{2}+1$$

Find \(f+g, f-g,\) fg, and \(\frac{f}{8} .\) Determine the domain for each function. $$f(x)=\frac{3 x+1}{x^{2}-25}, g(x)=\frac{2 x-4}{x^{2}-25}$$

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 \(f^{-1}\). $$f(x)=(x-1)^{2}, x \geq 1$$

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 \(f\). $$f(x)=x^{2}, g(x)=x^{2}-2$$