Chapter 1

Yes or No? If No , give a reason. (Disregard any value that makes a denominator zero.) (a) Is the expression \(\frac{x(x+1)}{(x+1)^{2}}\) equal to \(\frac{x}{x+1} ?\) (b) Is the expression \(\sqrt{x^{2}+25}\) equal to \(x+5 ?\)

Each equation, is \(y\) directly proportional, inversely proportional, or not proportional to \(x ?\). (a) \(y=\frac{3}{x+1}\) (b) \(y=\frac{3}{x}\)

The slope of a vertical line is _________. The equation of the vertical line passing through \((2,3)\) is ____________.

What is a logical first step in solving the inequality? (a) \(3 x \leq 7\) (b) \(5 x-2 \geq 1\) (c) \(|3 x+2| \leq 8\)

Find the missing power in the following calculation: \(5^{1 / 3} \cdot 5=5\)

The graph of the equation \((x-1)^{2}+(y-2)^{2}=9\) is a circle with center (_____ , _____) and radius __________.

The equation \((x+1)^{2}-5(x+1)+6=0\) is of ______ type. To solve the equation, we set \(W=\) ______ The resulting quadratic equation is ______ .

Solve the equation both algebraically and graphically. $$\frac{1}{2} x-3=6+2 x$$

The formula \(d=r t\) models the distance \(d\) traveled by an object moving at the constant rate \(r\) in time \(t .\) Find formulas for the following quantities. \(r=\)_____ \(t=\) _____

Yes or No? If \(\mathrm{No},\) give a reason. Is the sum of a complex number and its complex conjugate a real number?

The Special Factoring Formula for the "difference of squares" is \(A^{2}-B^{2}=\) ____, So \(4 x^{2}-25\) factors as ____.

Yes or No? If No , give a reason. (Disregard any value that makes a denominator zero.) (a) Is the expression \(\frac{3+a}{3}\) equal to \(1+\frac{a}{3} ?\) (b) Is the expression \(\frac{2}{4+x}\) equal to \(\frac{1}{2}+\frac{2}{x} ?\)

Yes or No? If No , give a reason. Assume that \(a\) and \(b\) are nonzero real numbers. (a) Is the sum of two rational numbers always a rational number? (b) Is the sum of two irrational numbers always an irrational number?

Write an equation that expresses the statement. \(T\) varies directly as \(x\)

Let \(S=\left\\{-5,-1,0, \frac{2}{3}, \frac{5}{6}, 1, \sqrt{5}, 3,5\right\\}\) Determine which elements of \(S\) satisfy the inequality. $$-2+3 x \geq \frac{1}{3}$$

Yes or No? If No, give a reason. (a) Is the graph of \(y=-3\) a horizontal line? (b) Is the graph of \(x=-3\) a vertical line? (c) Does a line perpendicular to a horizontal line have slope \(0 ?\) (d) Does a line perpendicular to a vertical line have slope \(0 ?\)

(a) If a graph is symmetric with respect to the x-axis and 1a, b2 is on the graph, then (_____ , _______) is also on the graph. (b) If a graph is symmetric with respect to the y-axis and 1a, b2 is on the graph, then (______ , _____) is also on the graph. (c) If a graph is symmetric about the origin and 1a, b2 is on the graph, then (______ , _____) is also on the graph.

Yes or No? If No, give a reason. (a) Is the expression \(\left(\frac{2}{3}\right)^{-2}\) equal to \(\frac{3}{4} ?\) (b) Is there a difference between \((-5)^{4}\) and \(-5^{4} ?\)

Solve the equation both algebraically and graphically. $$\frac{2}{x}+\frac{1}{2 x}=7$$

Using Variables Express the given quantity in terms of the indicated variable. The sum of three consecutive integers; \(n=\) first integer of the three.

Find the real and imaginary parts of the complex number. $$5-7 i$$

The Special Factoring Formula for a "perfect square" is A^{2}+2 A B+B^{2}=\quad \text { So } x^{2}+10 x+25 factors as ____.

Find the domain of the expression. $$4 x^{2}-10 x+3$$

Yes or No? If No , give a reason. Assume that \(a\) and \(b\) are nonzero real numbers. (a) Is \(a-b\) equal to \(b-a ?\) (b) Is \(-2(a-5)\) equal to \(-2 a-10 ?\)

Write an equation that expresses the statement. \(P\) is directly proportional to \(w\)

Let \(S=\left\\{-5,-1,0, \frac{2}{3}, \frac{5}{6}, 1, \sqrt{5}, 3,5\right\\}\) Determine which elements of \(S\) satisfy the inequality. $$1-2 x \geq 5 x$$

Sketch a graph of the lines \(y=-3\) and \(x=-3 .\) Are the lines perpendicular?

Yes or No? If No, give a reason. (a) Is the expression \(\left(x^{2}\right)^{3}\) equal to \(x^{5} ?\) (b) Is the expression \(\left(2 x^{4}\right)^{3}\) equal to \(2 x^{12} ?\) (c) Is the expression \(\sqrt{4 a^{2}}\) equal to \(2 a ?\) (d) Is the expression \(\sqrt{a^{2}+4}\) equal to \(a+2 ?\)

Solve the equation both algebraically and graphically. $$\frac{4}{x+2}-\frac{6}{2 x}=\frac{5}{2 x+4}$$

Using Variables Express the given quantity in terms of the indicated variable. The sum of three consecutive integers; \(n=\) middle integer of the three.

Find the real and imaginary parts of the complex number. $$-6+4 i$$

Yes or No? II No, give a reason. (a) Is the expression \((x+5)^{2}\) equal to \(x^{2}+25 ?\) (b) When you expand \((x+a)^{2},\) where \(a \neq 0,\) do you get three terms? (c) Is the expression \((x+5)(x-5)\) equal to \(x^{2}-25 ?\) (d) When you expand \((x+a)(x-a),\) where \(a \neq 0,\) do you get two terms?

Find the domain of the expression. $$-x^{4}+x^{3}+9 x$$

Yes or No? If No , give a reason. Assume that \(a\) and \(b\) are nonzero real numbers. (a) Is the distance between any two different real numbers always positive? (b) Is the distance between \(a\) and \(b\) the same as the distance between \(b\) and \(a\) ?

Write an equation that expresses the statement. \(v\) is inversely proportional to \(z\)

Write each radical expression using exponents, and each exponential expression using radicals. Radical expression = \(\frac{1}{\sqrt{3}}\) Exponential expression = ?

Yes or No? If No, give a reason. If the graph of an equation is symmetric with respect to both the \(x\) - and \(y\) -axes, is it necessarily symmetric with respect to the origin?

Let \(S=\left\\{-5,-1,0, \frac{2}{3}, \frac{5}{6}, 1, \sqrt{5}, 3,5\right\\}\) Determine which elements of \(S\) satisfy the inequality. $$1<2 x-4 \leq 7$$

Find the slope of the line through \(P\) and \(Q .\) \(P(-1,2), Q(0,0)\)

Solution? Determine whether the given value is a solution of the equation. \(4 x+7=9 x-3\) (a) \(x=-2\) (b) \(x=2\)

Solve the equation both algebraically and graphically. $$x^{2}-32=0$$

Using Variables Express the given quantity in terms of the indicated variable. The sum of three consecutive even integers; \(n=\) first integer of the three.

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\begin{array}{llll}\text { Polynomial } & \text { Type } & \text { Terms } & \text { Degree } \\ \hline 5 x^{3}+6 & & &\end{array}$$

Find the real and imaginary parts of the complex number. $$\frac{-2-5 i}{3}$$

Find the domain of the expression. $$\frac{x^{2}-1}{x-3}$$

Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c) rational numbers (d) irrational numbers $$\left\\{-1.5,0, \frac{5}{3}, \sqrt{7}, 2.71,-\pi, 3.1 \overline{4}, 100,-8\right\\}$$

Write an equation that expresses the statement. \(w\) is proportional to the product of \(m\) and \(n\)

Write each radical expression using exponents, and each exponential expression using radicals. Radical expression = \(\sqrt[3]{7^{2}}\) Exponential expression = ?

Yes or No? If No, give a reason. If the graph of an equation is symmetric with respect to both the \(x\) - and \(y\) -axes, is it necessarily symmetric with respect to the origin?

Let \(S=\left\\{-5,-1,0, \frac{2}{3}, \frac{5}{6}, 1, \sqrt{5}, 3,5\right\\}\) Determine which elements of \(S\) satisfy the inequality. $$-2 \leq 3-x < 2$$