91Ó°ÊÓ

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

(Hint: To solve for a variable involving an nth root, raise both sides of the equation to the nth power: \((\sqrt[n]{y})^{n}=y .\) ) $$ f(x)=\sqrt[3]{x}+1 $$

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. $$(x+2)^{2}+y^{2}=16$$

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

(Hint: To solve for a variable involving an nth root, raise both sides of the equation to the nth power: \((\sqrt[n]{y})^{n}=y .\) ) $$ f(x)=\sqrt[3]{x-1} $$

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=x^{2}-2 $$

Graph each equation in a rectangular coordinate system. \(y-0\)

f and g are defined by the following tables. Use the tables to evaluate each composite function. $$\begin{array}{cc}x & f(x) \\ \hline-1 & 1 \\ 0 & 4 \\ 1 & 5 \\ 2 & -1 \end{array}$$ $$\begin{array}{cc}x & g(x) \\ \hline-1 & 0 \\ 1 & 1 \\ 4 & 2 \\ 10 & -1 \end{array}$$ $$ f(g(1)) $$

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

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{aligned}0 & \text { if } & x &<-4 \\\\-x & \text { if } &-4 & \leq x<0 \\\x^{2} & \text { if } & x & \geq 0\end{aligned}\right.$$