Chapter 2

Evaluate each piecewise function at the given values of the independent variable. $$h(x)=\left\\{\begin{array}{ccc}\frac{x^{2}-25}{x-5} & \text { if } & x \neq 5 \\\10 & \text { if } & x-5\end{array}\right.$$ $$a. h(7)$$ $$b. h(0)$$ $$c. h(5)$$

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 graphts, describe how the graph of \(g\) is related to the graph of \(f\) $$ f(x)--2 x, g(x)--2 x+3 $$

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Determine the value of \(A\) so that the line whose equation is \(A x+y-2-0\) is perpendicular to the line containing the points \((1,-3)\) and \((-2,4)\).

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 r function. \(f(x)-\frac{3}{4} x-2\)

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

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 graphts, describe how the graph of \(g\) is related to the graph of \(f\) $$ f(x)-x^{2}, g(x)-x^{2}+1 $$

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

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. $$(x-2)^{2}+(y-3)^{2}=16$$

Give the slope and \(y\) -intercept of each line Whose equation is given. Then graph the r function. \(f(x)-\frac{3}{4} x-3\)

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

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 graphts, describe how the graph of \(g\) is related to the graph of \(f\) $$ f(x)-x^{2}, g(x)-x^{2}-2 $$

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 \(f^{-1}\). $$ f(x)=x^{3}-1 $$

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. $$(x+3)^{2}+(y-2)^{2}=4$$

Give the slope and \(y\) -intercept of each line Whose equation is given. Then graph the r function. \(y--\frac{3}{5} x+7\)

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

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 \(f^{-1}\). $$ f(x)=x^{3}+1 $$

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. $$(x+1)^{2}+(y-4)^{2}=25$$

Give the slope and \(y\) -intercept of each line Whose equation is given. Then graph the r function. \(y--\frac{2}{5} x+6\)

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{lll}1 x & \text { if } & x \leq 0 \\\3 & \text { if } & x>0\end{array}\right.$$

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 \(f^{-1}\). $$ f(x)=(x+2)^{3} $$

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

Give the slope and \(y\) -intercept of each line Whose equation is given. Then graph the r function. \(g(x)--\frac{1}{2} x\)

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{ll}x+3 & \text { if } x<-2 \\\x-3 & \text { if } x \geq-2\end{array}\right.$$

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 graphts, describe how the graph of \(g\) is related to the graph of \(f\) $$ f(x)-x^{3}, g(x)-x^{3}+2 $$

Find \(f+g, f-g,\) fg, and \(\frac{f}{x}\). Determine the \(d o^{2}\) $$ f(x)=\sqrt{x+4}, g(x)=\sqrt{x-1} $$

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 \(f^{-1}\). $$ f(x)=(x-2)^{3} $$

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

Give the slope and \(y\) -intercept of each line Whose equation is given. Then graph the r function. \(g(x)--\frac{1}{3} x\)

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{lll}x+2 & \text { if } & x<-3 \\\x-2 & \text { if } & x \geq-3\end{array}\right.$$

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 graphts, describe how the graph of \(g\) is related to the graph of \(f\) $$ f(x)-x^{3}, g(x)-x^{3}-1 $$

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

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

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{rll}3 & \text { if } & x \leq-1 \\\\-3 & \text { if } & x>-1\end{array}\right.$$

(Hint: To solve for a variable involving an nth root, raise both sides of the equation to the nth power: \((\sqrt[n]{y})^{n}=y .\) ) $$ f(x)=\sqrt{x}+2 $$

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

Graph each equation in a rectangular coordinate system. \(y=4\)

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{rll}4 & \text { if } & x \leq-1 \\\\-4 & \text { if } & x>-1\end{array}\right.$$

(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. $$(x+1)^{2}+y^{2}=25$$

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. $$f(x)=\left\\{\begin{array}{rll}-1 x^{2} & \text { if } & x<1 \\\2 x+1 & \text { if } & x \geq 1\end{array}\right.$$

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

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

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. $$f(x)=\left\\{\begin{aligned}0 & \text { if } & x &<-4 \\\\-x & \text { if } &-4 & \leq x<0 \\\x^{2} & \text { if } & x & \geq 0\end{aligned}\right.$$

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