Question 1

Sketch the graph of the equation $$4 x ^ { 3 } + 4$$ .

Accepted Answer

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

Question 2

Find the x- and y-intercepts of the graph of the equation $$y ^ { 2 } = 8 x + 5$$ .

Accepted Answer

A) x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$ 
y-intercept: $( 0 , - \sqrt { 5 } )$ 
B)  x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$
Y-intercept: $( 0 , \pm \sqrt { 5 } )$. 
C) x-intercept: $\left( 0 , \frac { 5 } { 8 } \right)$ 
y-intercept: $( 0 , \pm \sqrt { 5 } )$ 
D) x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$ 
y-intercept: $( 0 , \sqrt { 5 } )$ 
E) x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$ 
y-intercept: $( 0 , \sqrt { 5 } )$. 
A) x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$ 
y-intercept: $( 0 , - \sqrt { 5 } )$ 
B)  x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$
Y-intercept: $( 0 , \pm \sqrt { 5 } )$. 
C) x-intercept: $\left( 0 , \frac { 5 } { 8 } \right)$ 
y-intercept: $( 0 , \pm \sqrt { 5 } )$ 
D) x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$ 
y-intercept: $( 0 , \sqrt { 5 } )$ 
E) x-intercept: $\left( \frac { 5 } { 8 } , 0 \right)$ 
y-intercept: $( 0 , \sqrt { 5 } )$.

Question 3

Determine which of the following point lies on the graph of the equation.$$x ^ { 2 } + y ^ { 2 } = 5$$

Accepted Answer

A) (3,1) 
B) (2,3) 
C) (4,1) 
D) (2,1) 
E) (2,2) 
A) (3,1) 
B) (2,3) 
C) (4,1) 
D) (2,1) 
E) (2,2)

Question 4

Find the value of x that corresponds to y = 7 in the graph of the equation 4x - 3y = -37.

Accepted Answer

A) 4 
B) -16 
C) -3 
D) 3 
E) -4 
A) 4 
B) -16 
C) -3 
D) 3 
E) -4

Question 5

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. $$y = \sqrt { x - 2 }$$

Accepted Answer

A) x-intercept: (2,0) y-intercept: none
No symmetry
   
B) x-intercept: (2,0) y-intercept: none
No symmetry   
C) x-intercept: (2,0) y-intercept: (0, $\sqrt { 2 }$ )
No symmetry   
D) x-intercept: (-2,0) y-intercept: none
No symmetry
   
E) x-intercept: (-2,0) y-intercept: none
No symmetry
   
A) x-intercept: (2,0) y-intercept: none
No symmetry
   
B) x-intercept: (2,0) y-intercept: none
No symmetry   
C) x-intercept: (2,0) y-intercept: (0, $\sqrt { 2 }$ )
No symmetry   
D) x-intercept: (-2,0) y-intercept: none
No symmetry
   
E) x-intercept: (-2,0) y-intercept: none
No symmetry

Question 6

Graph the circle $$( x + 2 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$$

Accepted Answer

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

Question 7

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $3 x + 2 y ^ { 6 } = 0$

Accepted Answer

A) Symmetric with respect to the origin. 
B) No symmetry. 
C) Symmetric with respect to the y-axis. 
D) Symmetric with respect to the x-axis. 
A) Symmetric with respect to the origin. 
B) No symmetry. 
C) Symmetric with respect to the y-axis. 
D) Symmetric with respect to the x-axis.

Question 8

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. $$y = x + 2$$

Accepted Answer

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

Question 9

Write the standard form of the equation of the circle with the given characteristics. 
Endpoints of a diameter: (2,2), (12,2)

Accepted Answer

A)  $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$ 
B)  $( x - 2 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$ 
C)  $( x + 2 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$ 
D)  $( x + 7 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$ 
E)  $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ 
A)  $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$ 
B)  $( x - 2 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$ 
C)  $( x + 2 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$ 
D)  $( x + 7 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$ 
E)  $( x - 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$

Question 10

Write the standard form of the equation of the circle with the given characteristics. 
Center:(3,1);Radius: 7

Accepted Answer

A)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 49$ 
B)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 7$ 
C)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + 7 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } = 0$ 
E)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } - 49 = 0$ 
A)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 49$ 
B)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 7$ 
C)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + 7 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } = 0$ 
E)  $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } - 49 = 0$

Question 11

A hospital purchases a new magnetic resonance imaging (MRI)machine for $600,000.The depreciated value y (reduced value)after t years is given by y = 600,000 - 20,000t,0 ≤ t ≤ 6.Sketch the graph of the equation.

Accepted Answer

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

Question 12

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $$y = x \sqrt { x + 2 }$$

Accepted Answer

A) Intercepts: (0,0), (-2,0)    
B) Intercepts: (0,0), (2,0)   
C) Intercepts: (0,0), (-2,0)    
D) Intercepts: (0,0), (-2,0)    
E) Intercepts: (0,0), (6,0)    
A) Intercepts: (0,0), (-2,0)    
B) Intercepts: (0,0), (2,0)   
C) Intercepts: (0,0), (-2,0)    
D) Intercepts: (0,0), (-2,0)    
E) Intercepts: (0,0), (6,0)

Question 13

Find the center and radius of the circle $x ^ { 2 } + y ^ { 2 } = 49$ .

Accepted Answer

A) center: (0,0),radius: 11 
B) center: (-1,1),radius: 11 
C) center: (0,0),radius: 7 
D) center: (-1,-1),radius: 7 
E) center: (-7,-11),radius: 7 
A) center: (0,0),radius: 11 
B) center: (-1,1),radius: 11 
C) center: (0,0),radius: 7 
D) center: (-1,-1),radius: 7 
E) center: (-7,-11),radius: 7

Question 14

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. $y = x ^ { 3 } - 6$

Accepted Answer

A) x- intercept: ( $\sqrt [ 3 ] { 6 }$ ,0) y- intercept: (0,±6)
No symmetry   
B) x- intercept: ( $\sqrt [ 3 ] { 6 }$ ,0) y- intercept: (0,-6)
No symmetry
   
C) x- intercept: ( $\sqrt [ 3 ] { 6 }$ ,0) y- intercept: (0,6)
No symmetry   
D) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ ,0) y- intercept: (0,6)
No symmetry
   
E) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ ,0) y- intercept: (0,±6)
No symmetry   
A) x- intercept: ( $\sqrt [ 3 ] { 6 }$ ,0) y- intercept: (0,±6)
No symmetry   
B) x- intercept: ( $\sqrt [ 3 ] { 6 }$ ,0) y- intercept: (0,-6)
No symmetry
   
C) x- intercept: ( $\sqrt [ 3 ] { 6 }$ ,0) y- intercept: (0,6)
No symmetry   
D) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ ,0) y- intercept: (0,6)
No symmetry
   
E) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ ,0) y- intercept: (0,±6)
No symmetry

Question 15

Graphically estimate the x- and y-intercepts of the graph. $$y = 81 - 9 x ^ { 2 }$$

Accepted Answer

A) x-intercept: (±3,0) y-intercept: (0,81) 
B) x-intercept: (3,0) y-intercept: (0,81) 
C) x-intercept: (-3,0) y-intercept: (0,81) 
D) x-intercept: (±3,0) y-intercept: (0,9) 
E) x-intercept: (0,3) y-intercept: (0,81) 
A) x-intercept: (±3,0) y-intercept: (0,81) 
B) x-intercept: (3,0) y-intercept: (0,81) 
C) x-intercept: (-3,0) y-intercept: (0,81) 
D) x-intercept: (±3,0) y-intercept: (0,9) 
E) x-intercept: (0,3) y-intercept: (0,81)

Question 16

You purchase a house for $250,000. The depreciated value, y, after x years is given by y = 250,000 – 12,500x. Sketch the graph of the equation given 0 ≤ x ≤ 8.

Accepted Answer

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

Question 17

The resistance y (in ohms)of 1,000 feet of solid copper wire at 68 degrees Fahrenheit can be approximated by the model $$y = \frac { 10,770 } { x ^ { 2 } } - 0.37 , \quad 5 \leq x \leq 100$$ where x is the diameter of the wire in mils (0.001 inch). Complete the table.
$$\begin{array} { | l | l | l | l | l | l | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & & & & & \
\hline
\end{array}$$
Round the answer to two decimal places.

Accepted Answer

A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 1.54 & 3.19 & 1.83 & 4.95 \
\hline
\end{array}$$ 
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 4.95 & 3.19 & 1.54 & 1.83 \
\hline
\end{array}$$ 
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 4.95 & 1.83 & 3.19 & 1.54 \
\hline
\end{array}$$ 
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 3.19 & 4.95 & 1.83 & 1.54 \
\hline
\end{array}$$ 
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 4.95 & 3.19 & 1.83 & 1.54 \
\hline
\end{array}$$ 
A) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 1.54 & 3.19 & 1.83 & 4.95 \
\hline
\end{array}$$ 
B) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 4.95 & 3.19 & 1.54 & 1.83 \
\hline
\end{array}$$ 
C) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 4.95 & 1.83 & 3.19 & 1.54 \
\hline
\end{array}$$ 
D) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 3.19 & 4.95 & 1.83 & 1.54 \
\hline
\end{array}$$ 
E) $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 15 & 45 & 55 & 70 & 75 \
\hline y & 47.50 & 4.95 & 3.19 & 1.83 & 1.54 \
\hline
\end{array}$$

Question 18

Write the standard form of the equation of the circle with the given characteristics. center: (-5,-4);solution point: (-3,-7)

Accepted Answer

A)  $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 13$ 
B)  $( x - 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 1$ 
C)  $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 13$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 17$ 
E)  $( x + 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 17$ 
A)  $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 13$ 
B)  $( x - 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 1$ 
C)  $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 13$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 17$ 
E)  $( x + 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 17$

Question 19

Determine which of the following point lies on the graph of the equation. 
Y = |x - 2| + 4

Accepted Answer

A) (5,7) 
B) (5,9) 
C) (5,8) 
D) (8,7) 
E) (6,7) 
A) (5,7) 
B) (5,9) 
C) (5,8) 
D) (8,7) 
E) (6,7)

Question 20

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. 
Y = 2 - |x|

Accepted Answer

A) x- intercept: (±2,0) y- intercept: (0,2)
Y-axis symmetry
   
B) x- intercept: (-2,0) y- intercept: (0,2)
Y-axis symmetry   
C) x- intercept: (2,0) y- intercept: (0,±2)
Y-axis symmetry   
D) x- intercept: (2,0) y- intercept: (0,2)
Y-axis symmetry   
E) x- intercept: (-2,0) y- intercept: (0,2)
Y-axis symmetry   
A) x- intercept: (±2,0) y- intercept: (0,2)
Y-axis symmetry
   
B) x- intercept: (-2,0) y- intercept: (0,2)
Y-axis symmetry   
C) x- intercept: (2,0) y- intercept: (0,±2)
Y-axis symmetry   
D) x- intercept: (2,0) y- intercept: (0,2)
Y-axis symmetry   
E) x- intercept: (-2,0) y- intercept: (0,2)
Y-axis symmetry

Exam 2: Graphs of Equations

Sketch the graph of the equation 4x3+44 x ^ { 3 } + 44x3+4 .

Find the x- and y-intercepts of the graph of the equation y2=8x+5y ^ { 2 } = 8 x + 5y2=8x+5 .

Determine which of the following point lies on the graph of the equation. x2+y2=5x ^ { 2 } + y ^ { 2 } = 5x2+y2=5

Find the value of x that corresponds to y = 7 in the graph of the equation 4x - 3y = -37.

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. y=x−2y = \sqrt { x - 2 }y=x−2​

Graph the circle (x+2)2+(y−5)2=9( x + 2 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9(x+2)2+(y−5)2=9

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. 3x+2y6=03 x + 2 y ^ { 6 } = 03x+2y6=0

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. y=x+2y = x + 2y=x+2

Write the standard form of the equation of the circle with the given characteristics. Endpoints of a diameter: (2,2), (12,2)

Write the standard form of the equation of the circle with the given characteristics. Center:(3,1);Radius: 7

A hospital purchases a new magnetic resonance imaging (MRI)machine for $600,000.The depreciated value y (reduced value)after t years is given by y = 600,000 - 20,000t,0 ≤ t ≤ 6.Sketch the graph of the equation.

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. y=xx+2y = x \sqrt { x + 2 }y=xx+2​

Find the center and radius of the circle x2+y2=49x ^ { 2 } + y ^ { 2 } = 49x2+y2=49 .

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. y=x3−6y = x ^ { 3 } - 6y=x3−6

Graphically estimate the x- and y-intercepts of the graph. y=81−9x2y = 81 - 9 x ^ { 2 }y=81−9x2

You purchase a house for $250,000. The depreciated value, y, after x years is given by y = 250,000 – 12,500x. Sketch the graph of the equation given 0 ≤ x ≤ 8.

Write the standard form of the equation of the circle with the given characteristics. center: (-5,-4);solution point: (-3,-7)

Determine which of the following point lies on the graph of the equation. Y = |x - 2| + 4

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. Y = 2 - |x|

Rectangular Coordinates

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

Nonlinear Inequalities

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

Ellipses

Sketch the graph of the equation $4 x ^ { 3 } + 4$ .

Find the x- and y-intercepts of the graph of the equation $y ^ { 2 } = 8 x + 5$ .

Determine which of the following point lies on the graph of the equation. $x ^ { 2 } + y ^ { 2 } = 5$

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. $y = \sqrt { x - 2 }$

Graph the circle $( x + 2 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $3 x + 2 y ^ { 6 } = 0$

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. $y = x + 2$

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $y = x \sqrt { x + 2 }$

Find the center and radius of the circle $x ^ { 2 } + y ^ { 2 } = 49$ .

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. $y = x ^ { 3 } - 6$

Graphically estimate the x- and y-intercepts of the graph. $y = 81 - 9 x ^ { 2 }$ $Graphically estimate the x- and y-intercepts of the graph. y = 81 - 9 x ^ { 2 }$