Question 1

Which inequality corresponds to the given graph?

Accepted Answer

A)  $x - 1 < 0$ 
B)  $x - 1 \geq 0$ 
C)  $x + 1 \leq 0$ 
D)  $x - 1 \leq 0$ 
E)  $x + 1 < 0$ 
A)  $x - 1 < 0$ 
B)  $x - 1 \geq 0$ 
C)  $x + 1 \leq 0$ 
D)  $x - 1 \leq 0$ 
E)  $x + 1 < 0$

Question 2

A dietician is asked to design a special diet supplement using two foods. Each ounce of food Each ounce of food X contains 30 units of calcium and each ounce of food Y contains 20 units of calcium. The minimum daily requirement in the diet is 80 units of calcium. Sketch a graph of the solution of the linear inequality that represents the different numbers of units of food X and food Y required.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Use the graph of $f ( x ) = x ^ { 2 }$ to write a function that represents the graph, $g ( x )$ seen below.

Accepted Answer

A)  $g ( x ) = - x ^ { 2 } + 5$ 
B)  $g ( x ) = - ( x + 5 ) ^ { 2 } + 5$ 
C)  $g ( x ) = x ^ { 2 } + 5$ 
D)  $g ( x ) = - x ^ { 2 } - 5$ 
E)  $g ( x ) = - ( x + 5 ) ^ { 2 }$ 
A)  $g ( x ) = - x ^ { 2 } + 5$ 
B)  $g ( x ) = - ( x + 5 ) ^ { 2 } + 5$ 
C)  $g ( x ) = x ^ { 2 } + 5$ 
D)  $g ( x ) = - x ^ { 2 } - 5$ 
E)  $g ( x ) = - ( x + 5 ) ^ { 2 }$

Question 4

Plot the points on a rectangular coordinate system. $\left( - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) , ( 1,0 )$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

A warehouse for storing chairs and tables has 45 square feet of floor space. Each chair requires 15 square feet of floor space and each table requires 5 square feet of floor space. Sketch a graph of the solution of the inequality where x is the number of chairs and y is the number of tables.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

A store is offering a 45% discount on all items in its inventory. Find the sales price of an item that has a list price of $135 .

Accepted Answer

A) $ 104.63 
B) $ 74.25 
C) $ 119.81 
D) $ 128.93 
E) $ 60.75 
A) $ 104.63 
B) $ 74.25 
C) $ 119.81 
D) $ 128.93 
E) $ 60.75

Question 7

Determine the domain and range of the graph of the function $g ( x ) = x ^ { 3 } - 5$ .

Accepted Answer

A) The domain is all real numbers x such that $x \geq 0$ . The range is all real numbers y . 
B) The domain is all real numbers x such that $x \geq - 5$ . The range is all real numbers y . 
C) The domain is all real numbers x such that $x \leq 0$ . The range is all real numbers y such that $y \geq - 5$ . 
D) The domain is all real numbers x . The range is all real numbers y such that $y \geq - 5$ . 
E) The domain is all real numbers x . The range is all real numbers y . 
A) The domain is all real numbers x such that $x \geq 0$ . The range is all real numbers y . 
B) The domain is all real numbers x such that $x \geq - 5$ . The range is all real numbers y . 
C) The domain is all real numbers x such that $x \leq 0$ . The range is all real numbers y such that $y \geq - 5$ . 
D) The domain is all real numbers x . The range is all real numbers y such that $y \geq - 5$ . 
E) The domain is all real numbers x . The range is all real numbers y .

Question 8

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. Use the Vertical Line Test to determine if T is a function of t .

Accepted Answer

A) T is a function of t . 
B) T is not a function of t . 
A) T is a function of t . 
B) T is not a function of t .

Question 9

Compete the table and use the results to sketch the graph of the equation $y = x ^ { 2 } - 1$ 
$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 2 & - 1 & 0 & 1 & 2 \
\hline y & & & & & \
\hline
\end{array}$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Write an equation of the line that passes through the points (4,-2) and (1,7) . Write the equation in general form.

Accepted Answer

A)  $y = - \frac { 1 } { 3 } x + 10$ 
B)  $y = 3 x - 14$ 
C)  $y = - 3 x + 10$ 
D)  $y = 3 x + 10$ 
E)  $y = \frac { 1 } { 3 } x - 14$ 
A)  $y = - \frac { 1 } { 3 } x + 10$ 
B)  $y = 3 x - 14$ 
C)  $y = - 3 x + 10$ 
D)  $y = 3 x + 10$ 
E)  $y = \frac { 1 } { 3 } x - 14$

Question 11

Sketch the graph of $y = 4 x + 8$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Find the x - and y -intercepts of the graph of the equation $- 2 x - 4 y - 56 = 0$ .

Accepted Answer

A) x -intercept: 2 y -intercept: 4 
B) x -intercept: 28 y -intercept: -14 
C) x -intercept: -14 y -intercept: 28 
D) x -intercept: 14 y -intercept: 28 
E) x -intercept: -28 y -intercept: -14 
A) x -intercept: 2 y -intercept: 4 
B) x -intercept: 28 y -intercept: -14 
C) x -intercept: -14 y -intercept: 28 
D) x -intercept: 14 y -intercept: 28 
E) x -intercept: -28 y -intercept: -14

Question 13

Determine if $\{ ( 0 , - 6 ) , ( 1 , - 12 ) , ( 2 , - 11 ) , ( 3,3 ) , ( 4,12 ) \}$ represents a function.

Accepted Answer

A) The relation represents a function. 
B) The relation does not represent a function. 
A) The relation represents a function. 
B) The relation does not represent a function.

Question 14

Graph the equation $y = 2 - x$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Use the rule of correspondence to write a set of ordered pairs that represents the cubes of integers between 3 and 7 .

Accepted Answer

A)  $\{ ( 27,3 ) , ( 64,4 ) , ( 125,5 ) , ( 216,6 ) , ( 343,7 ) \}$ 
B)  $\{ ( 3,27 ) , ( 4,64 ) , ( 5,125 ) , ( 6,216 ) , ( 7,343 ) \}$ 
C)  $\{ ( 3,9 ) , ( 4,16 ) , ( 5,25 ) , ( 6,36 ) , ( 7,49 ) \}$ 
D)  $\{ ( 3,27 ) , ( 4,64 ) , ( 5,125 ) , ( 6,216 ) , ( 7,49 ) \}$ 
E)  $\{ ( 3,27 ) , ( 4,64 ) , ( 5,125 ) , ( 6,36 ) , ( 7,343 ) \}$ 
A)  $\{ ( 27,3 ) , ( 64,4 ) , ( 125,5 ) , ( 216,6 ) , ( 343,7 ) \}$ 
B)  $\{ ( 3,27 ) , ( 4,64 ) , ( 5,125 ) , ( 6,216 ) , ( 7,343 ) \}$ 
C)  $\{ ( 3,9 ) , ( 4,16 ) , ( 5,25 ) , ( 6,36 ) , ( 7,49 ) \}$ 
D)  $\{ ( 3,27 ) , ( 4,64 ) , ( 5,125 ) , ( 6,216 ) , ( 7,49 ) \}$ 
E)  $\{ ( 3,27 ) , ( 4,64 ) , ( 5,125 ) , ( 6,36 ) , ( 7,343 ) \}$

Question 16

Use a graphing calculator (with a standard viewing window)to graph the equation $y = 3 - | x + 2 |$ .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

A train travels at a speed of $75$ miles per hour. Write the distance d traveled by the train as function of time t in hours, and use it to find d (in miles)when the value of $t = 4$ hours.

Accepted Answer

A)  $d ( 4 ) = 1200$ miles 
B)  $d ( 4 ) = 75$ miles 
C)  $d ( 4 ) = 150$ miles 
D)  $d ( 4 ) = 16$ miles 
E)  $d ( 4 ) = 300$ miles 
A)  $d ( 4 ) = 1200$ miles 
B)  $d ( 4 ) = 75$ miles 
C)  $d ( 4 ) = 150$ miles 
D)  $d ( 4 ) = 16$ miles 
E)  $d ( 4 ) = 300$ miles

Question 18

Match the equation $y = \frac { 3 } { 2 } \pi + 3$ with its graph.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature T, in degrees Fahrenheit, is given in terms of t, the time on a 24 hour clock, as shown in the figure. The thermostat is then reprogrammed to produce a temperature H where $H ( t ) = T ( t ) - 2$ . Explain how this changes the temperature of the house.

Accepted Answer

A) The temperature of the house during the day will be 2 degrees cooler, and night will be 2 degrees warmer. 
B) The temperature of the house during the day and night will be 2 degrees cooler. 
C) lowers the temperature of the house 2 hours later at night, and warms up the temperature of the house 2 hours later in the morning 
D) The temperature of the house during the day will be 2 degrees warmer, and night will be 2 degrees cooler. 
E) The temperature of the house during the day and night will be 2 degrees warmer. 
A) The temperature of the house during the day will be 2 degrees cooler, and night will be 2 degrees warmer. 
B) The temperature of the house during the day and night will be 2 degrees cooler. 
C) lowers the temperature of the house 2 hours later at night, and warms up the temperature of the house 2 hours later in the morning 
D) The temperature of the house during the day will be 2 degrees warmer, and night will be 2 degrees cooler. 
E) The temperature of the house during the day and night will be 2 degrees warmer.

Question 20

Write an equation of a line passing through the points (-2,4) and (11,4) .

Accepted Answer

A)  y=0 
B)  y=4 
C)  x=4 
D)  x=-2 
E)  x=11 
A)  y=0 
B)  y=4 
C)  x=4 
D)  x=-2 
E)  x=11

Which inequality corresponds to the given graph?

Use the graph of $f ( x ) = x ^ { 2 }$ to write a function that represents the graph, $g ( x )$ seen below. $Use the graph of f ( x ) = x ^ { 2 } to write a function that represents the graph, g ( x ) seen below.$

Plot the points on a rectangular coordinate system. $\left( - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) , ( 1,0 )$

A warehouse for storing chairs and tables has 45 square feet of floor space. Each chair requires 15 square feet of floor space and each table requires 5 square feet of floor space. Sketch a graph of the solution of the inequality where x is the number of chairs and y is the number of tables.

A store is offering a 45% discount on all items in its inventory. Find the sales price of an item that has a list price of $135 .

Determine the domain and range of the graph of the function $g ( x ) = x ^ { 3 } - 5$ . $Determine the domain and range of the graph of the function g ( x ) = x ^ { 3 } - 5 .$

Compete the table and use the results to sketch the graph of the equation $y = x ^ { 2 } - 1$ x -2 -1 0 1 2 y

Write an equation of the line that passes through the points (4,-2) and (1,7) . Write the equation in general form.

Sketch the graph of $y = 4 x + 8$ .

Find the x - and y -intercepts of the graph of the equation $- 2 x - 4 y - 56 = 0$ .

Determine if $\{ ( 0 , - 6 ) , ( 1 , - 12 ) , ( 2 , - 11 ) , ( 3,3 ) , ( 4,12 ) \}$ represents a function.

Graph the equation $y = 2 - x$ .

Use the rule of correspondence to write a set of ordered pairs that represents the cubes of integers between 3 and 7 .

Use a graphing calculator (with a standard viewing window)to graph the equation $y = 3 - | x + 2 |$ .

A train travels at a speed of $75$ miles per hour. Write the distance d traveled by the train as function of time t in hours, and use it to find d (in miles)when the value of $t = 4$ hours.

Match the equation $y = \frac { 3 } { 2 } \pi + 3$ with its graph.

Write an equation of a line passing through the points (-2,4) and (11,4) .

Fundamentals of Algebra

Linear Equations and Inequalities

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 3: Graphs and Functions

Which inequality corresponds to the given graph?

Use the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to write a function that represents the graph, g(x)g ( x )g(x) seen below.

Plot the points on a rectangular coordinate system. (−32,−52),(1,0)\left( - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) , ( 1,0 )(−23​,−25​),(1,0)

A warehouse for storing chairs and tables has 45 square feet of floor space. Each chair requires 15 square feet of floor space and each table requires 5 square feet of floor space. Sketch a graph of the solution of the inequality where x is the number of chairs and y is the number of tables.

A store is offering a 45% discount on all items in its inventory. Find the sales price of an item that has a list price of $135 .

Determine the domain and range of the graph of the function g(x)=x3−5g ( x ) = x ^ { 3 } - 5g(x)=x3−5 .

Compete the table and use the results to sketch the graph of the equation y=x2−1y = x ^ { 2 } - 1y=x2−1 x -2 -1 0 1 2 y

Write an equation of the line that passes through the points (4,-2) and (1,7) . Write the equation in general form.

Sketch the graph of y=4x+8y = 4 x + 8y=4x+8 .

Find the x - and y -intercepts of the graph of the equation −2x−4y−56=0- 2 x - 4 y - 56 = 0−2x−4y−56=0 .

Determine if {(0,−6),(1,−12),(2,−11),(3,3),(4,12)}\{ ( 0 , - 6 ) , ( 1 , - 12 ) , ( 2 , - 11 ) , ( 3,3 ) , ( 4,12 ) \}{(0,−6),(1,−12),(2,−11),(3,3),(4,12)} represents a function.

Graph the equation y=2−xy = 2 - xy=2−x .

Use the rule of correspondence to write a set of ordered pairs that represents the cubes of integers between 3 and 7 .

Use a graphing calculator (with a standard viewing window)to graph the equation y=3−∣x+2∣y = 3 - | x + 2 |y=3−∣x+2∣ .

A train travels at a speed of 757575 miles per hour. Write the distance d traveled by the train as function of time t in hours, and use it to find d (in miles)when the value of t=4t = 4t=4 hours.

Match the equation y=32π+3y = \frac { 3 } { 2 } \pi + 3y=23​π+3 with its graph.

Write an equation of a line passing through the points (-2,4) and (11,4) .

Fundamentals of Algebra

Linear Equations and Inequalities

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Use the graph of $f ( x ) = x ^ { 2 }$ to write a function that represents the graph, $g ( x )$ seen below. $Use the graph of f ( x ) = x ^ { 2 } to write a function that represents the graph, g ( x ) seen below.$

Plot the points on a rectangular coordinate system. $\left( - \frac { 3 } { 2 } , - \frac { 5 } { 2 } \right) , ( 1,0 )$

Determine the domain and range of the graph of the function $g ( x ) = x ^ { 3 } - 5$ . $Determine the domain and range of the graph of the function g ( x ) = x ^ { 3 } - 5 .$

Compete the table and use the results to sketch the graph of the equation $y = x ^ { 2 } - 1$ x -2 -1 0 1 2 y

Sketch the graph of $y = 4 x + 8$ .

Find the x - and y -intercepts of the graph of the equation $- 2 x - 4 y - 56 = 0$ .

Determine if $\{ ( 0 , - 6 ) , ( 1 , - 12 ) , ( 2 , - 11 ) , ( 3,3 ) , ( 4,12 ) \}$ represents a function.

Graph the equation $y = 2 - x$ .

Use a graphing calculator (with a standard viewing window)to graph the equation $y = 3 - | x + 2 |$ .

A train travels at a speed of $75$ miles per hour. Write the distance d traveled by the train as function of time t in hours, and use it to find d (in miles)when the value of $t = 4$ hours.

Match the equation $y = \frac { 3 } { 2 } \pi + 3$ with its graph.