Chapter 2

Find the midpoint of each line segment with the given endpoints. $$(\sqrt{18},-4)\( and \)(\sqrt{2}, 4)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-3,-1)\) and \((2,4)\)

Find the domain of each function. $$ f(x)-\frac{2 x+7}{x^{3}-5 x^{2}-4 x+20} $$

Find the midpoint of each line segment with the given endpoints. $$(\sqrt{50},-6)\( and \)(\sqrt{2}, 6)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-4)\) and \((1,-1)\)

Find the domain of each function. $$ f(x)-\frac{7 x+2}{x^{3}-2 x^{2}-9 x+18} $$

If two lines are parallel, describe the relationship between their slopes.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(0,0), r=7$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-3,-2)\) and \((3,6)\)

If two lines are perpendicular, describe the relationship between their slopes.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(0,0), r=8$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-3,6)\) and \((3,-2)\)

If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line's equation.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(3,2), r=5$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-3,-1)\) and \((4,-1)\)

A formula in the form \(y-m x+b\) models the average retail price, \(y,\) of a new car \(x\) years after \(2000 .\) Would you expect \(m\) to be positive, negative, or zero? Explain your answer.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(2,-1), r=4$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-5)\) and \((6,-5)\)

Find \(f+g, f-g,\) fg, and \(\frac{f}{x}\). Determine the $d o^{2}$$$ f(x)-x-6, g(x)-5 x^{2} $$

What is a secant line?

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-1,4), r=2$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((2,4)\) with \(x\) -intercept \(--2\)

evaluate each function at the given values of the independent variable and simplify. $$ f(x)-\frac{4 x^{2}-1}{x^{2}} $$ A. \(f(2)\) B. \(f(-2) \quad\) C. \(f(-x)\)

What is the average rate of change of a function?

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-3,5), r=3$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((1,-3)\) with \(x\) -intercept \(--1\)

a. Why are the lines whose equations are \(y-\frac{1}{3} x+1\) and \(y--3 x-2\) perpendicular? b. Use a graphing utility to graph the equations in a \([-10,10,1]\) by \([-10,10,1]\) viewing rectangle. Do the lines appear to be perpendicular? c. Now use the zoom square feature of your utility. Describe what happens to the graphs. Explain why this is so.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-3,-1), r=\sqrt{3}$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. \(x\) -intercept \(--\frac{1}{2}\) and \(y\) -intercept \(-4\)

Evaluate each piecewise function at the given values of the independent variable. $$f(x)=\left\\{\begin{array}{ll}3 x+5 & \text { if } x<0 \\\4 x+7 & \text { if } x \geq 0\end{array}\right.$$ $$a. f(-2)$$ $$b. f(0)$$ $$c. f(3)$$

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-5,-3), r=\sqrt{5}$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. \(x\) -intercept \(-4\) and \(y\) -intercept \(--2\)

Evaluate each piecewise function at the given values of the independent variable. $$f(x)=\left\\{\begin{array}{ll}6 x-1 & \text { if } x<0 \\\7 x+3 & \text { if } x \geq 0\end{array}\right.$$ $$a. f(-3)$$ $$b. f(0)$$ $$c. f(4)$$

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I have linear functions that model changes for men and women over the same time period. The functions have the same slope, so their graphs are parallel lines, indicating that the rate of change for men is the same as the rate of change for women.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-4,0), r=10$$

Evaluate each piecewise function at the given values of the independent variable. $$g(x)=\left\\{\begin{array}{ll}x+3 & \text { if } x \geq-3 \\\\-(x+3) & \text { if } x<-3\end{array}\right.$$ $$a. g(0)$$ $$b. g(-6)$$ $$c. g(-3)$$

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The graph of my function is not a straight line, so I cannot use slope to analyze its rates of change.

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-2,0), r=6$$

Evaluate each piecewise function at the given values of the independent variable. $$g(x)=\left\\{\begin{array}{ll}x+5 & \text { if } x \geq-5 \\\\-(x+5) & \text { if } x<-5\end{array}\right.$$ $$a. g(0)$$ $$b. g(-6)$$ $$c. g(-5)$$

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 \(f^{-1}\). $$ f(x)=x^{2}-4, x \geq 0 $$

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

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

Evaluate each piecewise function at the given values of the independent variable. $$h(x)=\left\\{\begin{array}{ll}\frac{x^{2}-9}{x-3} & \text { if } x \neq 3 \\\6 & \text { if } x-3\end{array}\right.$$ $$a. h(5)$$ $$b. h(0)$$ $$c. h(3)$$

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 \(f\) $$ f(x)--2 x, g(x)--2 x-1 $$

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 \(f^{-1}\). $$ f(x)=x^{2}-1, x \leq 0 $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. What is the slope of a line that is perpendicular to the line whose equation is \(A x+B y+C-0, A=0\) and \(B \neq 0 ?\)

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. $$x^{2}+y^{2}=49$$

Give the slope and \(y\) -intercept of each line Whose equation is given. Then graph the r function. \(f(x)--3 x+2\)