Question 1

Solve the inequality and graph the solution on the real number line.​ $$x ^ { 3 } - 3 x ^ { 2 } - x > - 3$$ ​

Accepted Answer

A)  $$( - 1,1 ) \cup ( 3 , \infty )$$   
B)  $$( - 1,1 ) \cup ( - 3 , \infty )$$   
C)  $$( - 1,1 ) \cup ( 3 , \infty )$$   
D)  $$( - 1,1 ) \cup ( - 3 , - \infty )$$   
E)  $$( - 1,1 ) \cup ( - 3 , \infty )$$   
A)  $$( - 1,1 ) \cup ( 3 , \infty )$$   
B)  $$( - 1,1 ) \cup ( - 3 , \infty )$$   
C)  $$( - 1,1 ) \cup ( 3 , \infty )$$   
D)  $$( - 1,1 ) \cup ( - 3 , - \infty )$$   
E)  $$( - 1,1 ) \cup ( - 3 , \infty )$$   A

Question 2

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the inequality. ​
Equation: $y = \frac { 1 } { 6 } x ^ { 2 } - 6 x + 1$ ​
Inequality: $y \leq 0$ ​

Accepted Answer

A) ​   $$x \leq - 1 - \sqrt { \frac { 4 } { 27 } } , 1 - \sqrt { \frac { 4 } { 27 } } \leq x \leq 1 + \sqrt { \frac { 4 } { 27 } }$$ 
B) ​   $$1 - \sqrt { \frac { 4 } { 27 } } \leq \mathrm { x } \leq 1 + \sqrt { \frac { 4 } { 27 } }$$ 
C) ​   $$x \leq 1 - \sqrt { \frac { 4 } { 27 } } , 1 + \sqrt { \frac { 4 } { 27 } } \leq x$$ 
D) ​   $$x \leq - 1 - \sqrt { \frac { 4 } { 27 } } , - 1 + \sqrt { \frac { 4 } { 27 } } \leq x$$ 
E) ​   $$- 1 - \sqrt { \frac { 4 } { 27 } } \leq x \leq - 1 + \sqrt { \frac { 4 } { 27 } }$$ 
A) ​   $$x \leq - 1 - \sqrt { \frac { 4 } { 27 } } , 1 - \sqrt { \frac { 4 } { 27 } } \leq x \leq 1 + \sqrt { \frac { 4 } { 27 } }$$ 
B) ​   $$1 - \sqrt { \frac { 4 } { 27 } } \leq \mathrm { x } \leq 1 + \sqrt { \frac { 4 } { 27 } }$$ 
C) ​   $$x \leq 1 - \sqrt { \frac { 4 } { 27 } } , 1 + \sqrt { \frac { 4 } { 27 } } \leq x$$ 
D) ​   $$x \leq - 1 - \sqrt { \frac { 4 } { 27 } } , - 1 + \sqrt { \frac { 4 } { 27 } } \leq x$$ 
E) ​   $$- 1 - \sqrt { \frac { 4 } { 27 } } \leq x \leq - 1 + \sqrt { \frac { 4 } { 27 } }$$ B

Question 3

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​
Equation: $y = x ^ { 3 } - x ^ { 2 } - 16 x + 16$ ​
Inequality: $y \leq 0$ ​

Accepted Answer

A) ​   ​ $$\begin{array} { l } 
\infty < x \leq 4 \
1 \leq x \leq 4
\end{array}$$ 
B) ​   ​ $$\begin{array} { l } 
\infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$$ 
C) ​   ​ $$\begin{array} { l } 
- \infty < x \leq - 4 \
- 1 \leq x \leq - 4
\end{array}$$ 
D) ​   $$\begin{array} { l } 
- \infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$$ 
E) ​   ​ $$- \infty < x \leq 4$$ 
A) ​   ​ $$\begin{array} { l } 
\infty < x \leq 4 \
1 \leq x \leq 4
\end{array}$$ 
B) ​   ​ $$\begin{array} { l } 
\infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$$ 
C) ​   ​ $$\begin{array} { l } 
- \infty < x \leq - 4 \
- 1 \leq x \leq - 4
\end{array}$$ 
D) ​   $$\begin{array} { l } 
- \infty < x \leq - 4 \
1 \leq x \leq 4
\end{array}$$ 
E) ​   ​ $$- \infty < x \leq 4$$ D

Question 4

Solve the inequality $36 x - x ^ { 3 } < 0$ and write the solution set in interval notation.

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 0,6 )$ 
B)  $( - 6,6 )$ 
C)  $( - \infty , 6 )$ 
D)  $( - 6,0 ) \cup ( 6 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( 0,6 )$ 
B)  $( - 6,6 )$ 
C)  $( - \infty , 6 )$ 
D)  $( - 6,0 ) \cup ( 6 , \infty )$ 
E)  $( - \infty , \infty )$

Question 5

Determine whether the statement is true or false.Justify your answer, the solution set of the inequality $\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 0$ is the entire set of real numbers.
​

Accepted Answer

A) False,the y -values are less than zero for all values of x. 
B) True,the y -values are greater than zero for all values of x. 
A) False,the y -values are less than zero for all values of x. 
B) True,the y -values are greater than zero for all values of x.

Question 6

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​
Equation: $y = \frac { 6 x } { x - 5 }$ ​
Inequality: $y \geq 8$ ​

Accepted Answer

A) ​   $$5 < x \leq - \frac { 10 } { 1 }$$ 
B) ​   $$5 < x \leq \frac { 10 } { 1 }$$ 
C) ​   $$5 < x$$ 
D) ​   $$5 < x \leq \frac { 10 } { 1 }$$ 
E) ​   $$6 < x \leq \frac { 10 } { 1 }$$ 
A) ​   $$5 < x \leq - \frac { 10 } { 1 }$$ 
B) ​   $$5 < x \leq \frac { 10 } { 1 }$$ 
C) ​   $$5 < x$$ 
D) ​   $$5 < x \leq \frac { 10 } { 1 }$$ 
E) ​   $$6 < x \leq \frac { 10 } { 1 }$$

Question 7

Solve the inequality and graph the solution on the real number line. ​​ $( x - 7 ) ^ { 2 } \geq 1$ ​

Accepted Answer

A)  $( - \infty , - 6 ] \cup [ - 8 , \infty )$   
B)  $( - \infty , 6 ] \cup [ 8 , \infty )$   
C)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
D)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
E)  $( - \infty , 6 ] \cup [ 8 , \infty )$   
A)  $( - \infty , - 6 ] \cup [ - 8 , \infty )$   
B)  $( - \infty , 6 ] \cup [ 8 , \infty )$   
C)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
D)  $( - \infty , 8 ] \cup [ 6 , \infty )$   
E)  $( - \infty , 6 ] \cup [ 8 , \infty )$

Question 8

Solve the inequality and graph the solution on the real number line.​ $x ^ { 2 } + x < 12$ ​

Accepted Answer

A)  $( - 4,3 )$   
B)  $( - 4,3 )$   
C)  $( 4,3 )$   
D)  $( - 4 , - 3 )$   
E)  $( - 4 , - 3 )$   
A)  $( - 4,3 )$   
B)  $( - 4,3 )$   
C)  $( 4,3 )$   
D)  $( - 4 , - 3 )$   
E)  $( - 4 , - 3 )$

Question 9

Find the interval(s)for b such that the following equation has at least one real solution​ $x ^ { 2 } + b x + 6 = 0$ . ​

Accepted Answer

A)  $( - \infty , - \sqrt { 24 } ] \cup [ \sqrt { 24 } , \infty )$ 
B)  $( - \infty , - \sqrt { 24 } ] \cap [ \sqrt { 24 } , \infty )$ 
C)  $( - \infty , \sqrt { 24 } ] \cup ( \sqrt { 24 } , \infty )$ 
D)  $( - \infty , - \sqrt { 24 } ) \cup [ - \sqrt { 24 } , \infty )$ 
E)  $( - \infty , \sqrt { 24 } ] \cap [ \sqrt { 24 } , \infty )$ 
A)  $( - \infty , - \sqrt { 24 } ] \cup [ \sqrt { 24 } , \infty )$ 
B)  $( - \infty , - \sqrt { 24 } ] \cap [ \sqrt { 24 } , \infty )$ 
C)  $( - \infty , \sqrt { 24 } ] \cup ( \sqrt { 24 } , \infty )$ 
D)  $( - \infty , - \sqrt { 24 } ) \cup [ - \sqrt { 24 } , \infty )$ 
E)  $( - \infty , \sqrt { 24 } ] \cap [ \sqrt { 24 } , \infty )$

Question 10

Find the key numbers of the expression.​ $\frac { 1 } { x - 7 } + 1$ ​

Accepted Answer

A) -6,7 
B) 6,7,1 
C) -6,-7 
D) 6,7 
E) 6,-7 
A) -6,7 
B) 6,7,1 
C) -6,-7 
D) 6,7 
E) 6,-7

Question 11

Find the interval(s)for b such that the following equation has at least one real solution and write a conjecture about the interval(s)based on the values of the coefficients​ $4 x ^ { 2 } + b x + 13 = 0$ . ​

Accepted Answer

A) $( - \infty , - 2 \sqrt { 52 } ] \cup [ 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ B) $( - \infty , - 2 \sqrt { 52 } ] \cup [ - 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c 0$ and $c > 0$ , $- b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ D) $( - \infty , 2 \sqrt { 52 } ] \cap [ 2 \sqrt { 52 } , \infty )$ If \[a 0\) , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ E) $( - \infty , - 2 \sqrt { 52 } ] \cap [ 2 \sqrt { 52 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ A) $( - \infty , - 2 \sqrt { 52 } ] \cup [ 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ B) $( - \infty , - 2 \sqrt { 52 } ] \cup [ - 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c 0$ and $c > 0$ , $- b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$ D) $( - \infty , 2 \sqrt { 52 } ] \cap [ 2 \sqrt { 52 } , \infty )$ If \[a 0\) , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$ E) $( - \infty , - 2 \sqrt { 52 } ] \cap [ 2 \sqrt { 52 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$

Question 12

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie? ​

Accepted Answer

A)  $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$ 
B)  $$177 \mathrm { ft } \leq L \leq 48 \mathrm { ft }$$ 
C)  $$49 \mathrm { ft } \leq L \leq 178 \mathrm { ft }$$ 
D)  $8050 \mathrm { ft } \leq L \leq 47 \mathrm { ft }$ 
E)  $46 \mathrm { ft } \leq L \leq 175 \mathrm { ft }$ 
A)  $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$ 
B)  $$177 \mathrm { ft } \leq L \leq 48 \mathrm { ft }$$ 
C)  $$49 \mathrm { ft } \leq L \leq 178 \mathrm { ft }$$ 
D)  $8050 \mathrm { ft } \leq L \leq 47 \mathrm { ft }$ 
E)  $46 \mathrm { ft } \leq L \leq 175 \mathrm { ft }$

Question 13

Determine whether the value of $x = - 1$ is a solution of the inequality.​ $\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1$ ​

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 14

Solve the inequality and graph the solution on the real number line.​ $$\frac { 1 } { x } \geq \frac { 1 } { x + 2 }$$ ​

Accepted Answer

A)  $$( - \infty , - 2 ) \cap ( 0 , \infty )$$ ​   
B)  $$( - \infty , - 2 ) \cup ( 0 , \infty )$$   
C)  $$( - \infty , 2 ) \cap ( 0 , \infty )$$   
D)  $$( \infty , 2 ) \cup ( 0 , \infty )$$   
E)  $$( - \infty , 2 ) \cup ( 0 , \infty )$$   
A)  $$( - \infty , - 2 ) \cap ( 0 , \infty )$$ ​   
B)  $$( - \infty , - 2 ) \cup ( 0 , \infty )$$   
C)  $$( - \infty , 2 ) \cap ( 0 , \infty )$$   
D)  $$( \infty , 2 ) \cup ( 0 , \infty )$$   
E)  $$( - \infty , 2 ) \cup ( 0 , \infty )$$

Question 15

Solve the inequality and write the solution set in interval notation.​ $x ^ { 3 } - 36 x \geq 0$ ​

Accepted Answer

A)  $[ - 6,0 ] \cup [ 6 , \infty ]$ 
B)  $[ - 6,0 ] \cup [ 6 , \infty )$ 
C)  $[ - 36,0 ] \cap [ 6 , \infty ]$ 
D)  $[ - 36,0 ] \cup [ - 6 , \infty )$ 
E)  $[ - 6,0 ] \cap [ 6 , \infty )$ 
A)  $[ - 6,0 ] \cup [ 6 , \infty ]$ 
B)  $[ - 6,0 ] \cup [ 6 , \infty )$ 
C)  $[ - 36,0 ] \cap [ 6 , \infty ]$ 
D)  $[ - 36,0 ] \cup [ - 6 , \infty )$ 
E)  $[ - 6,0 ] \cap [ 6 , \infty )$

Question 16

Solve the inequality and graph the solution on the real number line.​ $$\frac { x ^ { 2 } + x - 12 } { x } \geq 0$$ ​

Accepted Answer

A)  $$[ - 4,0 ) \cap [ 3 , \infty )$$   
B)  $$[ 4,0 ) \cup [ 3 , \infty )$$   
C)  $$[ 4,0 ) \cup [ - 3 , \infty )$$   
D)  $$[ - 4,0 ) \cap [ - 3 , \infty )$$   
E)  $$[ - 4,0 ) \cup [ 3 , \infty )$$   
A)  $$[ - 4,0 ) \cap [ 3 , \infty )$$   
B)  $$[ 4,0 ) \cup [ 3 , \infty )$$   
C)  $$[ 4,0 ) \cup [ - 3 , \infty )$$   
D)  $$[ - 4,0 ) \cap [ - 3 , \infty )$$   
E)  $$[ - 4,0 ) \cup [ 3 , \infty )$$

Question 17

Solve the inequality and graph the solution on the real number line.​ $$\frac { 4 x - 1 } { x } > 0$$ ​

Accepted Answer

A)  $$( - \infty , 0 ) \cup \left( \frac { 1 } { 4 } , \infty \right)$$   
B)  $$( - \infty , 0 ) \cup \left( - \frac { 1 } { 4 } , \infty \right)$$ ​   
C)  $$( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)$$   
D)  $$( - \infty , 0 ) \cap \left( \frac { 1 } { 4 } , \infty \right)$$   
E)  $$( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \infty \right)$$   
A)  $$( - \infty , 0 ) \cup \left( \frac { 1 } { 4 } , \infty \right)$$   
B)  $$( - \infty , 0 ) \cup \left( - \frac { 1 } { 4 } , \infty \right)$$ ​   
C)  $$( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)$$   
D)  $$( - \infty , 0 ) \cap \left( \frac { 1 } { 4 } , \infty \right)$$   
E)  $$( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \infty \right)$$

Question 18

Solve the inequality and graph the solution on the real number line.​ $$x ^ { 2 } - 10 x - 24 > 0$$ ​

Accepted Answer

A)  $$( - \infty , - 2 ) \cup ( 12 , \infty )$$   
B)  $$( - \infty , - 2 ) \cap ( - 12 , \infty )$$   
C)  $$( - \infty , - 2 ) \cup ( - \infty , - 12 , )$$   
D)  $$( \infty , - 2 ) \cup [ 12 , \infty )$$   
E)  $$( - \infty , 2 ] \cup ( 12 , \infty )$$   
A)  $$( - \infty , - 2 ) \cup ( 12 , \infty )$$   
B)  $$( - \infty , - 2 ) \cap ( - 12 , \infty )$$   
C)  $$( - \infty , - 2 ) \cup ( - \infty , - 12 , )$$   
D)  $$( \infty , - 2 ) \cup [ 12 , \infty )$$   
E)  $$( - \infty , 2 ] \cup ( 12 , \infty )$$

Question 19

Solve the inequality and graph the solution on the real number line.​ $$x ^ { 2 } + 5 x + 13 > 0$$ ​

Accepted Answer

A) $$x \geq - 13$$ B) $$x \leq 13$$ C) $$x > 5$$ D) $$x < - 5$$ E) All real numbers A) $$x \geq - 13$$ B) $$x \leq 13$$ C) $$x > 5$$ D) $$x < - 5$$ E) All real numbers

Question 20

Determine the intervals on which the following polynomial is entirely negative and those on which it is entirely positive. $- x ^ { 2 } - 2 x + 35$

Accepted Answer

A) entirely negative: $( - \infty , 6 )$ ;entirely positive: $( 6 , \infty )$ 
B) entirely negative: $( - \infty , - 7 ) , ( 5,6 )$ ;entirely positive: $( - 7,6 )$ 
C) entirely negative: $( - \infty , - 7 ) , ( 5 , \infty )$ ;entirely positive: $( - 7,5 )$ 
D) entirely negative: $( - 7,6 )$ ;entirely positive: $( 0 , \infty )$   
E) entirely negative: $( - \infty , 0 )$ ;entirely positive: $( 0 , \infty )$ 
A) entirely negative: $( - \infty , 6 )$ ;entirely positive: $( 6 , \infty )$ 
B) entirely negative: $( - \infty , - 7 ) , ( 5,6 )$ ;entirely positive: $( - 7,6 )$ 
C) entirely negative: $( - \infty , - 7 ) , ( 5 , \infty )$ ;entirely positive: $( - 7,5 )$ 
D) entirely negative: $( - 7,6 )$ ;entirely positive: $( 0 , \infty )$   
E) entirely negative: $( - \infty , 0 )$ ;entirely positive: $( 0 , \infty )$

Exam 17: Nonlinear Inequalities

Solve the inequality and graph the solution on the real number line.​ x3−3x2−x>−3x ^ { 3 } - 3 x ^ { 2 } - x > - 3x3−3x2−x>−3 ​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the inequality. ​ Equation: y=16x2−6x+1y = \frac { 1 } { 6 } x ^ { 2 } - 6 x + 1y=61​x2−6x+1 ​ Inequality: y≤0y \leq 0y≤0 ​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​ Equation: y=x3−x2−16x+16y = x ^ { 3 } - x ^ { 2 } - 16 x + 16y=x3−x2−16x+16 ​ Inequality: y≤0y \leq 0y≤0 ​

Solve the inequality 36x−x3<036 x - x ^ { 3 } < 036x−x3<0 and write the solution set in interval notation.

Determine whether the statement is true or false.Justify your answer, the solution set of the inequality 72x2+7x+14≥0\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 027​x2+7x+14≥0 is the entire set of real numbers. ​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. ​ Equation: y=6xx−5y = \frac { 6 x } { x - 5 }y=x−56x​ ​ Inequality: y≥8y \geq 8y≥8 ​

Solve the inequality and graph the solution on the real number line. ​​ (x−7)2≥1( x - 7 ) ^ { 2 } \geq 1(x−7)2≥1 ​

Solve the inequality and graph the solution on the real number line.​ x2+x<12x ^ { 2 } + x < 12x2+x<12 ​

Find the interval(s)for b such that the following equation has at least one real solution​ x2+bx+6=0x ^ { 2 } + b x + 6 = 0x2+bx+6=0 . ​

Find the key numbers of the expression.​ 1x−7+1\frac { 1 } { x - 7 } + 1x−71​+1 ​

Find the interval(s)for b such that the following equation has at least one real solution and write a conjecture about the interval(s)based on the values of the coefficients​ 4x2+bx+13=04 x ^ { 2 } + b x + 13 = 04x2+bx+13=0 . ​

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie? ​

Determine whether the value of x=−1x = - 1x=−1 is a solution of the inequality.​ 3x2x2+4<1\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1x2+43x2​<1 ​

Solve the inequality and graph the solution on the real number line.​ 1x≥1x+2\frac { 1 } { x } \geq \frac { 1 } { x + 2 }x1​≥x+21​ ​

Solve the inequality and write the solution set in interval notation.​ x3−36x≥0x ^ { 3 } - 36 x \geq 0x3−36x≥0 ​

Solve the inequality and graph the solution on the real number line.​ x2+x−12x≥0\frac { x ^ { 2 } + x - 12 } { x } \geq 0xx2+x−12​≥0 ​

Solve the inequality and graph the solution on the real number line.​ 4x−1x>0\frac { 4 x - 1 } { x } > 0x4x−1​>0 ​

Solve the inequality and graph the solution on the real number line.​ x2−10x−24>0x ^ { 2 } - 10 x - 24 > 0x2−10x−24>0 ​

Solve the inequality and graph the solution on the real number line.​ x2+5x+13>0x ^ { 2 } + 5 x + 13 > 0x2+5x+13>0 ​

Determine the intervals on which the following polynomial is entirely negative and those on which it is entirely positive. −x2−2x+35- x ^ { 2 } - 2 x + 35−x2−2x+35

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Solve the inequality and graph the solution on the real number line. $x ^ { 3 } - 3 x ^ { 2 } - x > - 3$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the inequality. Equation: $y = \frac { 1 } { 6 } x ^ { 2 } - 6 x + 1$ Inequality: $y \leq 0$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = x ^ { 3 } - x ^ { 2 } - 16 x + 16$ Inequality: $y \leq 0$

Solve the inequality $36 x - x ^ { 3 } < 0$ and write the solution set in interval notation.

Determine whether the statement is true or false.Justify your answer, the solution set of the inequality $\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 0$ is the entire set of real numbers.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 x } { x - 5 }$ Inequality: $y \geq 8$

Solve the inequality and graph the solution on the real number line. $( x - 7 ) ^ { 2 } \geq 1$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + x < 12$

Find the interval(s)for b such that the following equation has at least one real solution $x ^ { 2 } + b x + 6 = 0$ .

Find the key numbers of the expression. $\frac { 1 } { x - 7 } + 1$

Find the interval(s)for b such that the following equation has at least one real solution and write a conjecture about the interval(s)based on the values of the coefficients $4 x ^ { 2 } + b x + 13 = 0$ .

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie?

Determine whether the value of $x = - 1$ is a solution of the inequality. $\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1$

Solve the inequality and graph the solution on the real number line. $\frac { 1 } { x } \geq \frac { 1 } { x + 2 }$

Solve the inequality and write the solution set in interval notation. $x ^ { 3 } - 36 x \geq 0$

Solve the inequality and graph the solution on the real number line. $\frac { x ^ { 2 } + x - 12 } { x } \geq 0$

Solve the inequality and graph the solution on the real number line. $\frac { 4 x - 1 } { x } > 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } - 10 x - 24 > 0$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 5 x + 13 > 0$

Determine the intervals on which the following polynomial is entirely negative and those on which it is entirely positive. $- x ^ { 2 } - 2 x + 35$