Question 1

Find all numbers not in the domain of the function
-$f(x)=\frac{x-7}{2}$

Accepted Answer

A)  0 
B)  None 
C)  -7 
D)  7 
A)  0 
B)  None 
C)  -7 
D)  7

Question 2

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$m^{2}-5 m, m^{2}-11 m+30$

Accepted Answer

A)  $(m+1)^{2}$ 
B)  $m(m+1)(m-6)$ 
C)  $m(m-5)(m-6)$ 
D)  $\mathrm{m}(\mathrm{m}+1)^{2}$ 
A)  $(m+1)^{2}$ 
B)  $m(m+1)(m-6)$ 
C)  $m(m-5)(m-6)$ 
D)  $\mathrm{m}(\mathrm{m}+1)^{2}$

Question 3

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{x^{2}+x-6}{2 x^{2}-9 x-5}$

Accepted Answer

A)  $\frac{1}{2},-5 ;\left\{x \mid x \neq \frac{1}{2},-5\right\}$ 
B)  $-\frac{1}{2}, 5 ;\left\{x \mid x \neq-\frac{1}{2}, 5\right\}$ 
C)  $-3,2 ;\{x \mid x \neq-3,2\}$ 
D)  $-2,5 ;\{x \mid x \neq-2,5\}$ 
A)  $\frac{1}{2},-5 ;\left\{x \mid x \neq \frac{1}{2},-5\right\}$ 
B)  $-\frac{1}{2}, 5 ;\left\{x \mid x \neq-\frac{1}{2}, 5\right\}$ 
C)  $-3,2 ;\{x \mid x \neq-3,2\}$ 
D)  $-2,5 ;\{x \mid x \neq-2,5\}$

Question 4

Simplify the complex fraction.
-$$\frac{\frac{4}{x}-\frac{x}{4}}{\frac{1}{4}-\frac{1}{x}}$$

Accepted Answer

A)  $-(x-4)$ 
B)  $4 x(x+4)$ 
C)  $x+4$ 
D)  $-(x+4)$ 
A)  $-(x-4)$ 
B)  $4 x(x+4)$ 
C)  $x+4$ 
D)  $-(x+4)$

Question 5

Choose the equivalent form of the given formula relating the weight of an object and its distance from the fulcrum. $\mathrm{d} w=\mathrm{DW}$.

Accepted Answer

A)  $d=\frac{w}{D W}$ 
B)  $\mathrm{D}=\frac{\mathrm{dW}}{\mathrm{W}}$ 
C)  $w=\frac{d}{D W}$ 
D)  $\mathrm{D}=\frac{\mathrm{dw}}{\mathrm{W}}$ 
A)  $d=\frac{w}{D W}$ 
B)  $\mathrm{D}=\frac{\mathrm{dW}}{\mathrm{W}}$ 
C)  $w=\frac{d}{D W}$ 
D)  $\mathrm{D}=\frac{\mathrm{dw}}{\mathrm{W}}$

Question 6

Choose the equivalent form of the given formula for lateral area of a cylinder. $\mathrm{A}=2 \pi \mathrm{rh}$

Accepted Answer

A)  $r=\frac{2 A}{\pi h}$ 
B)  $\mathrm{h}=\frac{\mathrm{rA}}{2 \pi}$ 
C)  $h=\frac{\pi r}{2 A}$ 
D)  $r=\frac{A}{2 \pi h}$ 
A)  $r=\frac{2 A}{\pi h}$ 
B)  $\mathrm{h}=\frac{\mathrm{rA}}{2 \pi}$ 
C)  $h=\frac{\pi r}{2 A}$ 
D)  $r=\frac{A}{2 \pi h}$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Find all real numbers excluded from the domain of the function. Then give the domain, using set builder notation.
-$f(x)=\frac{x^{2}-5 x}{x^{2}-4 x-45}$

Accepted Answer

A)  $-9,5 ;\{x \mid x \neq-9,5\}$ 
B)  $-5,9 ;\{x \mid x \neq-5,9\}$ 
C)  $-5,5 ;\{x \mid x \neq-5,5\}$ 
D)  0,$5 ;\{x \mid x \neq 0,5\}$ 
A)  $-9,5 ;\{x \mid x \neq-9,5\}$ 
B)  $-5,9 ;\{x \mid x \neq-5,9\}$ 
C)  $-5,5 ;\{x \mid x \neq-5,5\}$ 
D)  0,$5 ;\{x \mid x \neq 0,5\}$

Question 8

Find all numbers that are not in the domain of the function. Then give the domain using set notation.
-$f(x)=\frac{12}{x^{2}+7 x-18}$

Accepted Answer

A)  $-9,2 ;\{x \mid x \neq-9,2\}$ 
B)  0 ; $\{x \mid x \neq 0\}$ 
C)  $-2,9 ;\{x \mid x \neq-2,9\}$ 
D)  $0,-9 ;\{x \mid x \neq 0,-9\}$ 
A)  $-9,2 ;\{x \mid x \neq-9,2\}$ 
B)  0 ; $\{x \mid x \neq 0\}$ 
C)  $-2,9 ;\{x \mid x \neq-2,9\}$ 
D)  $0,-9 ;\{x \mid x \neq 0,-9\}$

Question 9

Choose the one alternative that best completes the statement or answers the question.
Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as
potential solutions.
-$\frac{4}{x+17}+\frac{18}{x-6}=0$

Accepted Answer

A)  $-17,6,4,18$ 
B)  $17,-6$ 
C)  $17,-6,-4,-18$ 
D)  $-17,6$ 
A)  $-17,6,4,18$ 
B)  $17,-6$ 
C)  $17,-6,-4,-18$ 
D)  $-17,6$

Question 10

Express the rational expression in lowest terms.
-$\frac{a^{2}-6 a}{(a+2)(a-6)}$

Accepted Answer

A)  $\frac{a-6}{a+2}$ 
B)  $\frac{a^{2}}{a+2}$ 
C)  $\frac{a}{a+2}$ 
D)  $\frac{1}{a+2}$ 
A)  $\frac{a-6}{a+2}$ 
B)  $\frac{a^{2}}{a+2}$ 
C)  $\frac{a}{a+2}$ 
D)  $\frac{1}{a+2}$

Question 11

Add or subtract as indicated.
-$\frac{3}{10 x}+\frac{9}{14 x^{2}}$

Accepted Answer

A)  $\frac{108}{70 x^{2}}$ 
B)  $\frac{12}{140 x^{2}}$ 
C)  $\frac{3(7 x+15)}{70 x^{2}}$ 
D)  $\frac{12}{10 x+14 x^{2}}$ 
A)  $\frac{108}{70 x^{2}}$ 
B)  $\frac{12}{140 x^{2}}$ 
C)  $\frac{3(7 x+15)}{70 x^{2}}$ 
D)  $\frac{12}{10 x+14 x^{2}}$

Question 12

Give the first step in solving the given equation for $x$.
$\mathrm{y}+\mathrm{z}=\frac{\mathrm{x}}{\mathrm{x}-\mathrm{y}}$

Accepted Answer

The first step is to

Question 13

Tell whether or not the rational expressions are equivalent.
-$\frac{x-2}{2-x}, \frac{1}{x-2}$

Accepted Answer

A) True 
 B)False

Question 14

The average number of vehicles waiting in line at a toll booth of a super highway is modeled by the function $n(x)=\frac{x^{2}}{0.5(1-x)}$, where $x$ is a quantity between 0 and 1 known as the traffic intensity. To the nearest tenth, find the average number of vehicles waiting if the traffic intensity is 0.81 .

Accepted Answer

A)  6.9 vehicles 
B)  1.6 vehicles 
C)  3.5 vehicles 
D)  8.5 vehicles 
A)  6.9 vehicles 
B)  1.6 vehicles 
C)  3.5 vehicles 
D)  8.5 vehicles

Question 15

Solve the problem. Round your answer, as needed.
-A machine can fill 2856 boxes of cereal in 0.4 hour. How many boxes of cereal can it fill per hour?

Accepted Answer

A)  5712 boxes 
B)  1142 boxes 
C)  7140 boxes 
D)  2856 boxes 
A)  5712 boxes 
B)  1142 boxes 
C)  7140 boxes 
D)  2856 boxes

Question 16

Choose the one alternative that best completes the statement or answers the question.
Solve the problem. Round your answer, as needed.
-The total resistance in this electric circuit is given by the formula below. Find the total resistance for $\mathrm{a}=3, \mathrm{~b}=7, \mathrm{c}=6 \mathrm{ohms}$.
Total resistance $=\mathrm{a}+\frac{1}{\frac{1}{\mathrm{~b}}+\frac{1}{\mathrm{c}}}$.

Accepted Answer

A)  $3.31 \mathrm{ohms}$ 
B)  $9.77 \mathrm{ohms}$ 
C)  $6.23 \mathrm{ohms}$ 
D)  $6.00 \mathrm{ohms}$ 
A)  $3.31 \mathrm{ohms}$ 
B)  $9.77 \mathrm{ohms}$ 
C)  $6.23 \mathrm{ohms}$ 
D)  $6.00 \mathrm{ohms}$

Question 17

Assume that the expressions given are denominators of fractions. Find the least common denominator.
-$r^{2}+4 r+3, r^{2}+r$

Accepted Answer

A)  $r(r+3)(r+1)$ 
B)  $r(r+3)$ 
C)  $r(r+1)$ 
D)  $r(r+1)^{2}$ 
A)  $r(r+3)(r+1)$ 
B)  $r(r+3)$ 
C)  $r(r+1)$ 
D)  $r(r+1)^{2}$

Question 18

Write the rational expression in lowest terms.
-$\frac{5-m}{m-5}$

Accepted Answer

A)  Already in lowest terms 
B)  1 
C)  $-m$ 
D)  -1 
A)  Already in lowest terms 
B)  1 
C)  $-m$ 
D)  -1

Question 19

Express the rational expression in lowest terms.
-$\frac{(y+2)(y-6)}{(y-6)(y+9)}$

Accepted Answer

A)  $\frac{y+6}{y+3}$ 
B)  $\frac{2 y-6}{2 y+3}$ 
C)  $\frac{y+2}{y+9}$ 
D)  $\frac{y-2}{y-9}$ 
A)  $\frac{y+6}{y+3}$ 
B)  $\frac{2 y-6}{2 y+3}$ 
C)  $\frac{y+2}{y+9}$ 
D)  $\frac{y-2}{y-9}$

Question 20

$1+\frac{1}{x}=\frac{90}{x^{2}}$

Accepted Answer

A)  $\{9,10\}$ 
B)  $\left\{-\frac{1}{10}, \frac{1}{9}\right\}$ 
C)  $\{-9,10\}$ 
D)  $\{-10,9\}$ 
A)  $\{9,10\}$ 
B)  $\left\{-\frac{1}{10}, \frac{1}{9}\right\}$ 
C)  $\{-9,10\}$ 
D)  $\{-10,9\}$

Find all numbers not in the domain of the function - $f(x)=\frac{x-7}{2}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $m^{2}-5 m, m^{2}-11 m+30$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x^{2}+x-6}{2 x^{2}-9 x-5}$

Simplify the complex fraction. - $\frac{\frac{4}{x}-\frac{x}{4}}{\frac{1}{4}-\frac{1}{x}}$

Choose the equivalent form of the given formula relating the weight of an object and its distance from the fulcrum. $\mathrm{d} w=\mathrm{DW}$ .

Choose the equivalent form of the given formula for lateral area of a cylinder. $\mathrm{A}=2 \pi \mathrm{rh}$

Choose the one alternative that best completes the statement or answers the question. Find all real numbers excluded from the domain of the function. Then give the domain, using set builder notation. - $f(x)=\frac{x^{2}-5 x}{x^{2}-4 x-45}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{12}{x^{2}+7 x-18}$

Choose the one alternative that best completes the statement or answers the question. Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions. - $\frac{4}{x+17}+\frac{18}{x-6}=0$

Express the rational expression in lowest terms. - $\frac{a^{2}-6 a}{(a+2)(a-6)}$

Add or subtract as indicated. - $\frac{3}{10 x}+\frac{9}{14 x^{2}}$

Give the first step in solving the given equation for $x$ . $\mathrm{y}+\mathrm{z}=\frac{\mathrm{x}}{\mathrm{x}-\mathrm{y}}$

Tell whether or not the rational expressions are equivalent. - $\frac{x-2}{2-x}, \frac{1}{x-2}$

Solve the problem. Round your answer, as needed. -A machine can fill 2856 boxes of cereal in 0.4 hour. How many boxes of cereal can it fill per hour?

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $r^{2}+4 r+3, r^{2}+r$

Write the rational expression in lowest terms. - $\frac{5-m}{m-5}$

Express the rational expression in lowest terms. - $\frac{(y+2)(y-6)}{(y-6)(y+9)}$

$1+\frac{1}{x}=\frac{90}{x^{2}}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 7: Rational Expressions and Functions

Find all numbers not in the domain of the function - f(x)=x−72f(x)=\frac{x-7}{2}f(x)=2x−7​

Assume that the expressions given are denominators of fractions. Find the least common denominator. - m2−5m,m2−11m+30m^{2}-5 m, m^{2}-11 m+30m2−5m,m2−11m+30

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=x2+x−62x2−9x−5f(x)=\frac{x^{2}+x-6}{2 x^{2}-9 x-5}f(x)=2x2−9x−5x2+x−6​

Simplify the complex fraction. - 4x−x414−1x\frac{\frac{4}{x}-\frac{x}{4}}{\frac{1}{4}-\frac{1}{x}}41​−x1​x4​−4x​​

Choose the equivalent form of the given formula relating the weight of an object and its distance from the fulcrum. dw=DW\mathrm{d} w=\mathrm{DW}dw=DW .

Choose the equivalent form of the given formula for lateral area of a cylinder. A=2πrh\mathrm{A}=2 \pi \mathrm{rh}A=2πrh

Choose the one alternative that best completes the statement or answers the question. Find all real numbers excluded from the domain of the function. Then give the domain, using set builder notation. - f(x)=x2−5xx2−4x−45f(x)=\frac{x^{2}-5 x}{x^{2}-4 x-45}f(x)=x2−4x−45x2−5x​

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - f(x)=12x2+7x−18f(x)=\frac{12}{x^{2}+7 x-18}f(x)=x2+7x−1812​

Choose the one alternative that best completes the statement or answers the question. Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions. - 4x+17+18x−6=0\frac{4}{x+17}+\frac{18}{x-6}=0x+174​+x−618​=0

Express the rational expression in lowest terms. - a2−6a(a+2)(a−6)\frac{a^{2}-6 a}{(a+2)(a-6)}(a+2)(a−6)a2−6a​

Add or subtract as indicated. - 310x+914x2\frac{3}{10 x}+\frac{9}{14 x^{2}}10x3​+14x29​

Give the first step in solving the given equation for xxx . y+z=xx−y\mathrm{y}+\mathrm{z}=\frac{\mathrm{x}}{\mathrm{x}-\mathrm{y}}y+z=x−yx​

Tell whether or not the rational expressions are equivalent. - x−22−x,1x−2\frac{x-2}{2-x}, \frac{1}{x-2}2−xx−2​,x−21​

Solve the problem. Round your answer, as needed. -A machine can fill 2856 boxes of cereal in 0.4 hour. How many boxes of cereal can it fill per hour?

Assume that the expressions given are denominators of fractions. Find the least common denominator. - r2+4r+3,r2+rr^{2}+4 r+3, r^{2}+rr2+4r+3,r2+r

Write the rational expression in lowest terms. - 5−mm−5\frac{5-m}{m-5}m−55−m​

Express the rational expression in lowest terms. - (y+2)(y−6)(y−6)(y+9)\frac{(y+2)(y-6)}{(y-6)(y+9)}(y−6)(y+9)(y+2)(y−6)​

1+1x=90x21+\frac{1}{x}=\frac{90}{x^{2}}1+x1​=x290​

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Find all numbers not in the domain of the function - $f(x)=\frac{x-7}{2}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $m^{2}-5 m, m^{2}-11 m+30$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{x^{2}+x-6}{2 x^{2}-9 x-5}$

Simplify the complex fraction. - $\frac{\frac{4}{x}-\frac{x}{4}}{\frac{1}{4}-\frac{1}{x}}$

Choose the equivalent form of the given formula relating the weight of an object and its distance from the fulcrum. $\mathrm{d} w=\mathrm{DW}$ .

Choose the equivalent form of the given formula for lateral area of a cylinder. $\mathrm{A}=2 \pi \mathrm{rh}$

Choose the one alternative that best completes the statement or answers the question. Find all real numbers excluded from the domain of the function. Then give the domain, using set builder notation. - $f(x)=\frac{x^{2}-5 x}{x^{2}-4 x-45}$

Find all numbers that are not in the domain of the function. Then give the domain using set notation. - $f(x)=\frac{12}{x^{2}+7 x-18}$

Choose the one alternative that best completes the statement or answers the question. Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions. - $\frac{4}{x+17}+\frac{18}{x-6}=0$

Express the rational expression in lowest terms. - $\frac{a^{2}-6 a}{(a+2)(a-6)}$

Add or subtract as indicated. - $\frac{3}{10 x}+\frac{9}{14 x^{2}}$

Give the first step in solving the given equation for $x$ . $\mathrm{y}+\mathrm{z}=\frac{\mathrm{x}}{\mathrm{x}-\mathrm{y}}$

Tell whether or not the rational expressions are equivalent. - $\frac{x-2}{2-x}, \frac{1}{x-2}$

Assume that the expressions given are denominators of fractions. Find the least common denominator. - $r^{2}+4 r+3, r^{2}+r$

Write the rational expression in lowest terms. - $\frac{5-m}{m-5}$

Express the rational expression in lowest terms. - $\frac{(y+2)(y-6)}{(y-6)(y+9)}$

$1+\frac{1}{x}=\frac{90}{x^{2}}$