Question 1

Determine all possible quadrants in which the point can be located. Assume $x \neq 0$ and $y \neq 0$ . $( x , y ) , x + y < 0$

Accepted Answer

A) Quadrants $\text { II, III and IV }$ 
B) Quadrants II and III 
C) Quadrants $\text { I, II and IV }$ 
D) All quadrants 
E) Quadrants I and II 
A) Quadrants $\text { II, III and IV }$ 
B) Quadrants II and III 
C) Quadrants $\text { I, II and IV }$ 
D) All quadrants 
E) Quadrants I and II

Question 2

Evaluate and simplify $f ( x ) = \frac { x + 2 } { x - 3 }$ at $x = - \frac { 15 } { 2 }$ .

Accepted Answer

A)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 11 } { 21 }$ 
B)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 21 } { 11 }$ 
C)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 13 } { 18 }$ 
D)  $f \left( - \frac { 15 } { 2 } \right) = - \frac { 18 } { 13 }$ 
E)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 18 } { 13 }$ 
A)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 11 } { 21 }$ 
B)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 21 } { 11 }$ 
C)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 13 } { 18 }$ 
D)  $f \left( - \frac { 15 } { 2 } \right) = - \frac { 18 } { 13 }$ 
E)  $f \left( - \frac { 15 } { 2 } \right) = \frac { 18 } { 13 }$

Question 3

Determine whether the set of ordered pairs $\{ ( 3,8 ) , ( 2,8 ) , ( 3,17 ) \}$ represents a function from A to B , where $A = \{ 1,2,3 \}$ and $B = \{ 8,10,15,17 \}$ .

Accepted Answer

A) not a function from A to B 
B) a function from A to B 
A) not a function from A to B 
B) a function from A to B

Question 4

Determine the coordinates of the point labeled 2 .

Accepted Answer

A)  $( 3 , - 2 )$ 
B)  $( - 3,2 )$ 
C)  $( 3,2 )$ 
D)  $( - 2 , - 3 )$ 
E)  $( 2,3 )$ 
A)  $( 3 , - 2 )$ 
B)  $( - 3,2 )$ 
C)  $( 3,2 )$ 
D)  $( - 2 , - 3 )$ 
E)  $( 2,3 )$

Question 5

Which inequality corresponds to the given graph?

Accepted Answer

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

Question 6

Use the graph of f to sketch the graph of $y = f ( x + 1 )$ .

Accepted Answer

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

Question 7

Use a graphing calculator (with a standard viewing window)to graph the equation $y = - \frac { 1 } { 2 } x ^ { 2 } + 1$ .

Accepted Answer

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

Question 8

Sketch the graph of the linear inequality $\frac { x } { 2 } - \frac { y } { 3 } > 1$ .

Accepted Answer

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

Question 9

Match the correct equation with the given graph.

Accepted Answer

A)  $y = 2 - x ^ { 2 }$ 
B)  $y = 2 + x ^ { 2 }$ 
C)  $y = - 2 - x ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 }$ 
E)  $y = - 2 + x ^ { 2 }$ 
A)  $y = 2 - x ^ { 2 }$ 
B)  $y = 2 + x ^ { 2 }$ 
C)  $y = - 2 - x ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 }$ 
E)  $y = - 2 + x ^ { 2 }$

Question 10

Write an equation of the line that passes through the points $( - 1,1.6 )$ and $( - 3 , - 4.4 )$ . Write the equation in general form.

Accepted Answer

A)  $x - 3 y - 4.6 = 0$ 
B)  $3 x + y + 5.8 = 0$ 
C)  $- 3 x + y + 5.8 = 0$ 
D)  $- 3 x + y - 4.6 = 0$ 
E)  $x + 3 y - 4.6 = 0$ 
A)  $x - 3 y - 4.6 = 0$ 
B)  $3 x + y + 5.8 = 0$ 
C)  $- 3 x + y + 5.8 = 0$ 
D)  $- 3 x + y - 4.6 = 0$ 
E)  $x + 3 y - 4.6 = 0$

Question 11

A warehouse for storing chairs and tables has 950 square feet of floor space. Each chair requires 11 square feet of floor space and each table requires 18 square feet of floor space. Write a linear inequality for this space constraint where x is the number of chairs and y is the number of tables.

Accepted Answer

A)  $11 x + 18 y \leq 921$ 
B)  $18 x + 11 y \leq 950$ 
C)  $11 x + 7 y \leq 921$ 
D)  $11 x + 18 y \leq 950$ 
E)  $11 x + 18 y \geq 950$ 
A)  $11 x + 18 y \leq 921$ 
B)  $18 x + 11 y \leq 950$ 
C)  $11 x + 7 y \leq 921$ 
D)  $11 x + 18 y \leq 950$ 
E)  $11 x + 18 y \geq 950$

Question 12

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

Accepted Answer

A)  $g ( x ) = \sqrt { - x + 3 }$ 
B)  $g ( x ) = \sqrt { x - 3 }$ 
C)  $g ( x ) = - \sqrt { x + 3 }$ 
D)  $g ( x ) = \sqrt { x + 3 }$ 
E)  $g ( x ) = \sqrt { - x - 3 }$ 
A)  $g ( x ) = \sqrt { - x + 3 }$ 
B)  $g ( x ) = \sqrt { x - 3 }$ 
C)  $g ( x ) = - \sqrt { x + 3 }$ 
D)  $g ( x ) = \sqrt { x + 3 }$ 
E)  $g ( x ) = \sqrt { - x - 3 }$

Question 13

Sketch the graph of the equation $y = \frac { 2 } { 3 } x - 2$ and label three points on the graph.

Accepted Answer

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

Question 14

Graphically estimate the x- and y- intercepts, if any, of the graph.

Accepted Answer

A) x- intercept at -9 , y- intercept at -9 
B) x- intercept at -9 , no y- intercepts 
C) no x- intercepts, y- intercept at -9 
D) x- intercept at -9 , y- intercept at 9 
E) no intercepts 
A) x- intercept at -9 , y- intercept at -9 
B) x- intercept at -9 , no y- intercepts 
C) no x- intercepts, y- intercept at -9 
D) x- intercept at -9 , y- intercept at 9 
E) no intercepts

Question 15

Use the formula for slope to find the value of y such that the line through the points (1,-4) and (0,y) has slope of m=-2 .

Accepted Answer

A)  y=4 
B)  y=-4 
C)  y=-2 
D)  y=2 
E)  $y = 5$ 
A)  y=4 
B)  y=-4 
C)  y=-2 
D)  y=2 
E)  $y = 5$

Question 16

Find the midpoint of the line segment joining the points $( - 6,0 )$ and $( 8,4 )$ .

Accepted Answer

A)  $( 14,4 )$ 
B)  $( 1,4 )$ 
C)  $( 7,2 )$ 
D)  $( 1,2 )$ 
E)  $( 2,4 )$ 
A)  $( 14,4 )$ 
B)  $( 1,4 )$ 
C)  $( 7,2 )$ 
D)  $( 1,2 )$ 
E)  $( 2,4 )$

Question 17

Find the slope of the line passing through points (0,0) and (-5,-8) .

Accepted Answer

A)  $- \frac { 8 } { 5 }$ 
B)  $- \frac { 5 } { 8 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $\frac { 5 } { 8 }$ 
E)  $\frac { 8 } { 5 }$ 
A)  $- \frac { 8 } { 5 }$ 
B)  $- \frac { 5 } { 8 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $\frac { 5 } { 8 }$ 
E)  $\frac { 8 } { 5 }$

Question 18

Find the domain and the range of the relation $\{ ( 0,0 ) , ( 7 , - 7 ) , ( 5,12 ) , ( 9,9 ) , ( 10,9 ) \}$ .

Accepted Answer

A) Domain: $\{ 5,7,9,10 \}$ ; Range: $\{ - 7,9,12 \}$ 
B) Domain: $\{ - 7,0,9,9,12 \}$ ; Range: $\{ 0,5,7,9,10 \}$ 
C) Domain: $\{ 0,5,7,9,10 \}$ ; Range: $\{ - 7,0,9,12 \}$ 
D) Domain: $\{ - 7,0,9,12 \}$ ; Range: $\{ 0,5,7,9,10 \}$ 
E) Domain: $\{ 5,7,9,10 \}$ ; Range: $\{ - 7,9,9,12 \}$ 
A) Domain: $\{ 5,7,9,10 \}$ ; Range: $\{ - 7,9,12 \}$ 
B) Domain: $\{ - 7,0,9,9,12 \}$ ; Range: $\{ 0,5,7,9,10 \}$ 
C) Domain: $\{ 0,5,7,9,10 \}$ ; Range: $\{ - 7,0,9,12 \}$ 
D) Domain: $\{ - 7,0,9,12 \}$ ; Range: $\{ 0,5,7,9,10 \}$ 
E) Domain: $\{ 5,7,9,10 \}$ ; Range: $\{ - 7,9,9,12 \}$

Question 19

Find the x- and y- intercepts, if any, of $y = 18 - \frac { 2 } { 5 } x$ .

Accepted Answer

A) x- intercept at -45 , y- intercept at 18 
B) x- intercept at 18 , y- intercept at 45 
C) x- intercept at 45 , y- intercept at 18 
D) x- intercept at -18, y- intercept at 45 
E) no intercepts 
A) x- intercept at -45 , y- intercept at 18 
B) x- intercept at 18 , y- intercept at 45 
C) x- intercept at 45 , y- intercept at 18 
D) x- intercept at -18, y- intercept at 45 
E) no intercepts

Question 20

Determine which of the points is a solution of the inequality $4 x + 5 y > - 4$ .

Accepted Answer

A)  (10,-10) 
B)  (-4,-5) 
C)  (-2,-1) 
D)  (5,-10) 
E)  (-2,4) 
A)  (10,-10) 
B)  (-4,-5) 
C)  (-2,-1) 
D)  (5,-10) 
E)  (-2,4)

Determine all possible quadrants in which the point can be located. Assume $x \neq 0$ and $y \neq 0$ . $( x , y ) , x + y < 0$

Evaluate and simplify $f ( x ) = \frac { x + 2 } { x - 3 }$ at $x = - \frac { 15 } { 2 }$ .

Determine whether the set of ordered pairs $\{ ( 3,8 ) , ( 2,8 ) , ( 3,17 ) \}$ represents a function from A to B , where $A = \{ 1,2,3 \}$ and $B = \{ 8,10,15,17 \}$ .

Determine the coordinates of the point labeled 2 .

Which inequality corresponds to the given graph?

Use the graph of f to sketch the graph of $y = f ( x + 1 )$ .

Use a graphing calculator (with a standard viewing window)to graph the equation $y = - \frac { 1 } { 2 } x ^ { 2 } + 1$ .

Sketch the graph of the linear inequality $\frac { x } { 2 } - \frac { y } { 3 } > 1$ .

Match the correct equation with the given graph.

Write an equation of the line that passes through the points $( - 1,1.6 )$ and $( - 3 , - 4.4 )$ . Write the equation in general form.

A warehouse for storing chairs and tables has 950 square feet of floor space. Each chair requires 11 square feet of floor space and each table requires 18 square feet of floor space. Write a linear inequality for this space constraint where x is the number of chairs and y is the number of tables.

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

Sketch the graph of the equation $y = \frac { 2 } { 3 } x - 2$ and label three points on the graph.

Graphically estimate the x- and y- intercepts, if any, of the graph.

Use the formula for slope to find the value of y such that the line through the points (1,-4) and (0,y) has slope of m=-2 .

Find the midpoint of the line segment joining the points $( - 6,0 )$ and $( 8,4 )$ .

Find the slope of the line passing through points (0,0) and (-5,-8) .

Find the domain and the range of the relation $\{ ( 0,0 ) , ( 7 , - 7 ) , ( 5,12 ) , ( 9,9 ) , ( 10,9 ) \}$ .

Find the x- and y- intercepts, if any, of $y = 18 - \frac { 2 } { 5 } x$ .

Determine which of the points is a solution of the inequality $4 x + 5 y > - 4$ .

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

Determine all possible quadrants in which the point can be located. Assume x≠0x \neq 0x=0 and y≠0y \neq 0y=0 . (x,y),x+y<0( x , y ) , x + y < 0(x,y),x+y<0

Evaluate and simplify f(x)=x+2x−3f ( x ) = \frac { x + 2 } { x - 3 }f(x)=x−3x+2​ at x=−152x = - \frac { 15 } { 2 }x=−215​ .

Determine whether the set of ordered pairs {(3,8),(2,8),(3,17)}\{ ( 3,8 ) , ( 2,8 ) , ( 3,17 ) \}{(3,8),(2,8),(3,17)} represents a function from A to B , where A={1,2,3}A = \{ 1,2,3 \}A={1,2,3} and B={8,10,15,17}B = \{ 8,10,15,17 \}B={8,10,15,17} .

Determine the coordinates of the point labeled 2 .

Which inequality corresponds to the given graph?

Use the graph of f to sketch the graph of y=f(x+1)y = f ( x + 1 )y=f(x+1) .

Use a graphing calculator (with a standard viewing window)to graph the equation y=−12x2+1y = - \frac { 1 } { 2 } x ^ { 2 } + 1y=−21​x2+1 .

Sketch the graph of the linear inequality x2−y3>1\frac { x } { 2 } - \frac { y } { 3 } > 12x​−3y​>1 .

Match the correct equation with the given graph.

Write an equation of the line that passes through the points (−1,1.6)( - 1,1.6 )(−1,1.6) and (−3,−4.4)( - 3 , - 4.4 )(−3,−4.4) . Write the equation in general form.

A warehouse for storing chairs and tables has 950 square feet of floor space. Each chair requires 11 square feet of floor space and each table requires 18 square feet of floor space. Write a linear inequality for this space constraint where x is the number of chairs and y is the number of tables.

Use the graph of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ to write a function that represents the graph, g(x)g ( x )g(x) seen below.

Sketch the graph of the equation y=23x−2y = \frac { 2 } { 3 } x - 2y=32​x−2 and label three points on the graph.

Graphically estimate the x- and y- intercepts, if any, of the graph.

Use the formula for slope to find the value of y such that the line through the points (1,-4) and (0,y) has slope of m=-2 .

Find the midpoint of the line segment joining the points (−6,0)( - 6,0 )(−6,0) and (8,4)( 8,4 )(8,4) .

Find the slope of the line passing through points (0,0) and (-5,-8) .

Find the domain and the range of the relation {(0,0),(7,−7),(5,12),(9,9),(10,9)}\{ ( 0,0 ) , ( 7 , - 7 ) , ( 5,12 ) , ( 9,9 ) , ( 10,9 ) \}{(0,0),(7,−7),(5,12),(9,9),(10,9)} .

Find the x- and y- intercepts, if any, of y=18−25xy = 18 - \frac { 2 } { 5 } xy=18−52​x .

Determine which of the points is a solution of the inequality 4x+5y>−44 x + 5 y > - 44x+5y>−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

Determine all possible quadrants in which the point can be located. Assume $x \neq 0$ and $y \neq 0$ . $( x , y ) , x + y < 0$

Evaluate and simplify $f ( x ) = \frac { x + 2 } { x - 3 }$ at $x = - \frac { 15 } { 2 }$ .

Determine whether the set of ordered pairs $\{ ( 3,8 ) , ( 2,8 ) , ( 3,17 ) \}$ represents a function from A to B , where $A = \{ 1,2,3 \}$ and $B = \{ 8,10,15,17 \}$ .

Use the graph of f to sketch the graph of $y = f ( x + 1 )$ .

Use a graphing calculator (with a standard viewing window)to graph the equation $y = - \frac { 1 } { 2 } x ^ { 2 } + 1$ .

Sketch the graph of the linear inequality $\frac { x } { 2 } - \frac { y } { 3 } > 1$ .

Write an equation of the line that passes through the points $( - 1,1.6 )$ and $( - 3 , - 4.4 )$ . Write the equation in general form.

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

Sketch the graph of the equation $y = \frac { 2 } { 3 } x - 2$ and label three points on the graph.

Find the midpoint of the line segment joining the points $( - 6,0 )$ and $( 8,4 )$ .

Find the domain and the range of the relation $\{ ( 0,0 ) , ( 7 , - 7 ) , ( 5,12 ) , ( 9,9 ) , ( 10,9 ) \}$ .

Find the x- and y- intercepts, if any, of $y = 18 - \frac { 2 } { 5 } x$ .

Determine which of the points is a solution of the inequality $4 x + 5 y > - 4$ .