91Ó°ÊÓ

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. $$ (x+4)^{2}+(y+5)^{2}=36 $$

the domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$ f(x)=\left\\{\begin{array}{ccc} \frac{1}{2} x^{2} & \text { if } & x<1 \\ 2 x-1 & \text { if } & x \geq 1 \end{array}\right. $$

Graph the given square root functions, \(f\) and \(g,\) in the same rectangular coordinate system. Use the integer values of \(x\) given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of \(x\) that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of \(f\). $$ \begin{aligned} &f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and }\\\ &g(x)=\sqrt{x}+2 \quad(x=0,1,4,9) \end{aligned} $$

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+12 x-6 y-4=0 $$

Let $$\begin{aligned}&f(x)=2 x-5\\\&g(x)=4 x-1\\\&h(x)=x^{2}+x+2\end{aligned}$$ Evaluate the indicated function without finding an equation for the function. $$f^{-1}(1)$$

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} x^{2}+y^{2} &=16 \\ x-y &=4 \end{aligned} $$

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?

Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=|x|+4$$

write a piecewise function that models each cellphone billing plan. Then graph the function. \(\$ 60\) per month buys 450 minutes. Additional time costs \(\$ 0.35\) per minute.