Chapter 1

The endpoints of a line segment \(\overline{A B}\) are given. Sketch the reflection of \(\overline{A B}\) about (a) the \(x\) -axis; (b) the \(y\) -axis; and (c) the origin. \(A(1,4)\) and \(B(3,1)\)

Compute the slope of the line passing through the two given points. In Exercise \(3,\) include a sketch with your answers. (a) (-3,2),(1,-6) (b) (2,-5),(4,1) (c) (-2,7),(1,0) (d) (4,5),(5,8)

Determine whether the given point lies on the graph of the equation, as in Example \(1 .\) Note: You are not asked to draw the graph. $$(8,6) ; y=\frac{1}{2} x+3$$

Plot the points \((5,2),(-4,5),(-4,0),(-1,-1),\) and (5,-2)

Determine whether the given value is a solution of the equation. $$4 x-5=-13 ; x=-2$$

Evaluate each expression. $$|3|$$

Determine whether the number is a natural number, an integer, a rational number, or an irrational number. (Some numbers fit in more than one category.) The following facts will be helpful in some cases: Any number of the form \(\sqrt{n},\) where \(n\) is a natural number that is not a perfect square, is irrational. Also, the sum, difference, product, and quotient of an irrational number and a nonzero rational are all irrational. (For example, the following four numbers are irrational: \(\sqrt{6}\), \(\sqrt{10}-2,3 \sqrt{15},\) and \(-5 \sqrt{3} / 2,\) (a) -203 (b) \(203 / 2\)

The endpoints of a line segment \(\overline{A B}\) are given. Sketch the reflection of \(\overline{A B}\) about (a) the \(x\) -axis; (b) the \(y\) -axis; and (c) the origin. \(A(-1,-2)\) and \(B(-5,-2)\)

Compute the slope of the line passing through the two given points. In Exercise \(3,\) include a sketch with your answers. (a) (-3,0),(4,9) (b) (-1,2),(3,0) (c) \(\left(\frac{1}{2},-\frac{3}{5}\right),\left(\frac{3}{2}, \frac{3}{4}\right)\) (d) \(\left(\frac{17}{3},-\frac{1}{2}\right),\left(-\frac{1}{2}, \frac{17}{3}\right)\)

Determine whether the given point lies on the graph of the equation, as in Example \(1 .\) Note: You are not asked to draw the graph. $$\left(\frac{3}{3},-\frac{17}{5}\right) ; y=-\frac{2}{3} x-3$$

Draw the square \(A B C D\) with vertices (corners) \(A(1,0)\) \(B(0,1), C(-1,0),\) and \(D(0,-1)\)

Determine whether the given value is a solution of the equation. $$\frac{1}{x}=\frac{3}{x}-1 ; x=2$$

Evaluate each expression. $$3+|-3|$$

Determine whether the number is a natural number, an integer, a rational number, or an irrational number. (Some numbers fit in more than one category.) The following facts will be helpful in some cases: Any number of the form \(\sqrt{n},\) where \(n\) is a natural number that is not a perfect square, is irrational. Also, the sum, difference, product, and quotient of an irrational number and a nonzero rational are all irrational. (For example, the following four numbers are irrational: \(\sqrt{6}\), \(\sqrt{10}-2,3 \sqrt{15},\) and \(-5 \sqrt{3} / 2,\) (a) \(27 / 4\) (b) \(\sqrt{27 / 4}\)

The endpoints of a line segment \(\overline{A B}\) are given. Sketch the reflection of \(\overline{A B}\) about (a) the \(x\) -axis; (b) the \(y\) -axis; and (c) the origin. \(A(-2,-3)\) and \(B(2,-1)\)

Compute the slope of the line passing through the two given points. In Exercise \(3,\) include a sketch with your answers. (a) (1,1),(-1,-1) (b) (0,5),(-8,5)

Determine whether the given point lies on the graph of the equation, as in Example \(1 .\) Note: You are not asked to draw the graph. $$(4,3) ; 3 x^{2}+y^{2}=52$$

(a) Draw the right triangle \(P Q R\) with vertices \(P(1,0)\) \(Q(5,0),\) and \(R(5,3)\) (b) Use the formula for the area of a triangle, \(A=\frac{1}{2} b h\) to find the area of triangle \(P Q R\) in part (a).

Determine whether the given value is a solution of the equation. $$\frac{2}{y-1}-\frac{3}{y}=\frac{7}{y^{2}-y} ; y=-3$$

Evaluate each expression. $$|-6|$$

Determine whether the number is a natural number, an integer, a rational number, or an irrational number. (Some numbers fit in more than one category.) The following facts will be helpful in some cases: Any number of the form \(\sqrt{n},\) where \(n\) is a natural number that is not a perfect square, is irrational. Also, the sum, difference, product, and quotient of an irrational number and a nonzero rational are all irrational. (For example, the following four numbers are irrational: \(\sqrt{6}\), \(\sqrt{10}-2,3 \sqrt{15},\) and \(-5 \sqrt{3} / 2,\) (a) \(10^{6}\) (b) \(10^{6} / 10^{7}\)

The endpoints of a line segment \(\overline{A B}\) are given. Sketch the reflection of \(\overline{A B}\) about (a) the \(x\) -axis; (b) the \(y\) -axis; and (c) the origin. \(A(-3,-3)\) and \(B(-3,-1)\)

Determine whether the given point lies on the graph of the equation, as in Example \(1 .\) Note: You are not asked to draw the graph. $$(4,-2) ; 3 x^{2}+y^{2}=52$$

Determine whether the given value is a solution of the equation. $$(y-1)(y+5)=0 ; y=5$$

Evaluate each expression. $$-6-|-6|$$

The endpoints of a line segment \(\overline{A B}\) are given. Sketch the reflection of \(\overline{A B}\) about (a) the \(x\) -axis; (b) the \(y\) -axis; and (c) the origin. \(A(0,1)\) and \(B(3,1)\)

Determine whether the given point lies on the graph of the equation, as in Example \(1 .\) Note: You are not asked to draw the graph. $$(a, 4 a) ; y=4 x$$

Calculate the distance between the given points. (a) (0,0) and (-3,4) (b) (2,1) and (7,13)

Determine whether the given value is a solution of the equation. $$m^{2}+m-\frac{5}{16}=0 ; m=\frac{1}{4}$$

Evaluate each expression. $$|-1+3|$$

The endpoints of a line segment \(\overline{A B}\) are given. Sketch the reflection of \(\overline{A B}\) about (a) the \(x\) -axis; (b) the \(y\) -axis; and (c) the origin. \(A(-2,-2)\) and \(B(0,0)\)

Determine whether the given point lies on the graph of the equation, as in Example \(1 .\) Note: You are not asked to draw the graph. $$(a-1, a+1) ; y=x+2$$

Calculate the distance between the given points. (a) (-1,-3) and (-5,4) (b) (6,-2) and (-1,1)

Determine whether the given value is a solution of the equation. Verify that the numbers \(1+\sqrt{5}\) and \(1-\sqrt{5}\) both satisfy the equation \(x^{2}-2 x-4=0\)

Evaluate each expression. $$|-6+3|$$

Determine whether the number is a natural number, an integer, a rational number, or an irrational number. (Some numbers fit in more than one category.) The following facts will be helpful in some cases: Any number of the form \(\sqrt{n},\) where \(n\) is a natural number that is not a perfect square, is irrational. Also, the sum, difference, product, and quotient of an irrational number and a nonzero rational are all irrational. (For example, the following four numbers are irrational: \(\sqrt{6}\), \(\sqrt{10}-2,3 \sqrt{15},\) and \(-5 \sqrt{3} / 2,\) (a) \(\sqrt{99}\) (b) \(\sqrt{99}+1\)

(a) Solve the equation \(2 x-3 y=-3\) for \(y\) and then complete the following table. $$\begin{array}{lccccc} \hline x & -6 & -3 & 0 & 3 & 6 \\ \hline y & & & & & \\ \hline \end{array}$$ (b) Use your table from part (a) to graph the equation \(2 x-3 y=-3\)

Calculate the distance between the given points. (a) (-5,0) and (5,0) (b) (0,-8) and (0,1)

Solve each equation. $$2 x-3=-5$$

Evaluate each expression. $$\left|-\frac{4}{5}\right|-\frac{4}{5}$$

Graph the equation after determining the \(x\) - and \(y\) -intercepts and whether the graph possesses any of the three types of symmetry described on page 58 $$y=-x^{3}$$

(a) Solve the equation \(3 x+2 y=6\) for \(y\) and then complete the following table. $$\begin{array}{lccccc} \hline x & -4 & -2 & 0 & 2 & 4 \\ \hline y & & & & & \\ \hline \end{array}$$ (b) Use your table from part (a) to graph the equation \(3 x+2 y=6\)

Calculate the distance between the given points. (a) (-5,-3) and (-9,-6) (b) \(\left(\frac{2}{2}, 3\right)\) and \(\left(-2 \frac{1}{2},-1\right)\)

Solve each equation. $$2 m-1+3 m+5=6 m-8$$

Evaluate each expression. $$\left|\frac{4}{5}\right|-\frac{4}{5}$$

Determine whether the number is a natural number, an integer, a rational number, or an irrational number. (Some numbers fit in more than one category.) The following facts will be helpful in some cases: Any number of the form \(\sqrt{n},\) where \(n\) is a natural number that is not a perfect square, is irrational. Also, the sum, difference, product, and quotient of an irrational number and a nonzero rational are all irrational. (For example, the following four numbers are irrational: \(\sqrt{6}\), \(\sqrt{10}-2,3 \sqrt{15},\) and \(-5 \sqrt{3} / 2,\) \((3-\sqrt{2})+(3+\sqrt{2})\)

Graph the equation after determining the \(x\) - and \(y\) -intercepts and whether the graph possesses any of the three types of symmetry described on page 58 $$y=-1 / x$$

The graph of each equation is a straight line. Graph the equation after finding the \(x\)-and the \(y\) -intercepts. (since you are given that the graph is a line, you need only plot two points before drawing the line.) $$3 x+4 y=12$$

Calculate the distance between the given points. \((1, \sqrt{3}) \text { and }(-1,-\sqrt{3})\)

Solve each equation. $$1-(2 m+5)=-3 m$$