Chapter 2

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

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=x^{2}-1 $$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x+4 y+16=0$$

The domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$f(x)=\left\\{\begin{array}{ccc}0 & \text { if } & x<-3 \\\\-x & \text { if } & -3 \leq x<0 \\\x^{2}-1 & \text { if } & x \geq 0\end{array}\right.$$

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

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

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. $$x^{2}+y^{2}-10 x-6 y-30=0$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=4 x$$

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$ f(x)=4 x-3, g(x)-5 x^{2}-2 $$

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

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)-(x-1)^{2} $$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-4 x-12 y-9=0$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=7 x$$

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

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

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x-2 y-8=0$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=3 x+7$$

Graph each equation in a rectangular coordinate system. \(3 x-18-0\)

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)--(x-1)^{2} $$

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

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=6 x+1$$

Graph each equation in a rectangular coordinate system. \(3 x+12-0\)

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$ f(x)-x^{2}+1, g(x)=x^{2}-3 $$

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. $$ x^{2}-2 x+y^{2}-15=0 $$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=x^{2}$$

a. Rewrite the given equation in slope-intercept form. b. Give the slope and \(y\) -intercept. c. Use the slope and y-intercept to graph the linear function. \(3 x+y-5-0\)

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)-(x-1)^{2}+2 $$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}-6 y-7=0 $$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=2 x^{2}$$

a. Rewrite the given equation in slope-intercept form. b. Give the slope and \(y\) -intercept. c. Use the slope and y-intercept to graph the linear function. \(4 x+y-6-0\)

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$ f(x)-5 x-2, g(x)--x^{2}+4 x-1 $$

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

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}-x+2 y+1=0 $$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=x^{2}-4 x+3$$

a. Rewrite the given equation in slope-intercept form. b. Give the slope and \(y\) -intercept. c. Use the slope and y-intercept to graph the linear function. \(2 x+3 y-18-0\)

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)-\frac{1}{2}(x-1)^{2} $$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+x+y-\frac{1}{2}=0 $$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=x^{2}-5 x+8$$

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)-2(x-2)^{2}-1 $$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+3 x-2 y-1=0 $$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=2 x^{2}+x-1$$

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$ f(x)-2 x-3, g(x)-\frac{x+3}{2} $$

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)-\frac 12(x-1)^{2}-1 $$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}+3 x+5 y+\frac{9}{4}=0 $$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$f(x)=3 x^{2}+x+5$$

a. Rewrite the given equation in slope-intercept form. b. Give the slope and \(y\) -intercept. c. Use the slope and y-intercept to graph the linear function. \(6 x-5 y-20-0\)

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$ f(x)-6 x-3, g(x)-\frac{x+3}{6} $$

Begin by graphing the standard quadratic function, \(f(x)-x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)--2(x+1)^{2}+1 $$