Question 1

Determine which of the following point lies on the graph of the equation. 
Y = 3 - |x - 1|

Accepted Answer

A) (4,2) 
B) (6,0) 
C) (5,0) 
D) (4,0) 
E) (4,1) 
A) (4,2) 
B) (6,0) 
C) (5,0) 
D) (4,0) 
E) (4,1) D

Question 2

Find the x- and y-intercepts of the graph of the equation y = 36 - 6x.

Accepted Answer

A) x-intercept: (6,0) y-intercept: (0,-6) 
B) x-intercept: (36,0) y-intercept: (0,6) 
C) x-intercept: (-6,0) y-intercept: (0,-36) 
D) x-intercept: (36,0) y-intercept: (0,36) 
E) x-intercept: (6,0) y-intercept: (0,36) 
A) x-intercept: (6,0) y-intercept: (0,-6) 
B) x-intercept: (36,0) y-intercept: (0,6) 
C) x-intercept: (-6,0) y-intercept: (0,-36) 
D) x-intercept: (36,0) y-intercept: (0,36) 
E) x-intercept: (6,0) y-intercept: (0,36) E

Question 3

Determine which of the following point lies on the graph of the equation.$$y = \frac { 1 } { 3 } x ^ { 3 } - 3 x ^ { 2 }$$

Accepted Answer

A) (6,0) 
B) (7,6) 
C) (8,6) 
D) (6,7) 
E) (6,8) 
A) (6,0) 
B) (7,6) 
C) (8,6) 
D) (6,7) 
E) (6,8) A

Question 4

Find the graph of the equation. ?
F (x)= | x - 2 |

Accepted Answer

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

Question 5

Identify any intercepts and test for symmetry.Then sketch the graph of the equation.? $$y = x ^ { 2 } + 3$$ ?

Accepted Answer

A) x-intercept : none y-intercept : (0,3)
The graph has y-symmetry.?   
B) x-intercept : (0,0), (-3,0) y-intercept : (0,0)
No symmetry   
C) x-intercept : (0,0), (-3,0) y-intercept : (0,0)
No symmetry
?   
D) x-intercept : (0,0), (3,0) y-intercept : (0,0)
No symmetry
?   
E) x-intercept : (0,0), (3,0) y-intercept : (0,0)
No symmetry
?  
? 
A) x-intercept : none y-intercept : (0,3)
The graph has y-symmetry.?   
B) x-intercept : (0,0), (-3,0) y-intercept : (0,0)
No symmetry   
C) x-intercept : (0,0), (-3,0) y-intercept : (0,0)
No symmetry
?   
D) x-intercept : (0,0), (3,0) y-intercept : (0,0)
No symmetry
?   
E) x-intercept : (0,0), (3,0) y-intercept : (0,0)
No symmetry
?  
?

Question 6

Find the y-intercept of the graph of the equation y = 3x + 18.

Accepted Answer

A) (0,3) 
B) (18,0) 
C) (-6,0) 
D) (0,18) 
E) (0,-6) 
A) (0,3) 
B) (18,0) 
C) (-6,0) 
D) (0,18) 
E) (0,-6)

Question 7

Which of the following graphs are symmetric about the y-axis?

Accepted Answer

A)  $y = x ^ { 7 } - x ^ { 6 } + 18$ 
B)  $y = x ^ { 7 } - x ^ { 12 } + 18$ 
C)  $y = x ^ { 9 } - x ^ { 7 } + 18$ 
D)  $y = x ^ { 12 } - x ^ { 6 } + 18$ 
E)  $y = x ^ { 9 } + x ^ { 7 } + 18$ 
A)  $y = x ^ { 7 } - x ^ { 6 } + 18$ 
B)  $y = x ^ { 7 } - x ^ { 12 } + 18$ 
C)  $y = x ^ { 9 } - x ^ { 7 } + 18$ 
D)  $y = x ^ { 12 } - x ^ { 6 } + 18$ 
E)  $y = x ^ { 9 } + x ^ { 7 } + 18$

Question 8

Find the x- and y-intercepts of the graph of the equation $$y = | 13 x - 7 |$$ .

Accepted Answer

A) x-intercept: $\left( - \frac { 7 } { 13 } , 0 \right)$ y-intercept: (0,13) 
B)  x-intercept: $\left( - \frac { 13 } { 7 } , 0 \right)$
Y-intercept: (0,-7) 
C) x-intercept: (-7,0) y-intercept: (0,13) 
D) x-intercept: $\left( - \frac { 13 } { 7 } , 0 \right)$ y-intercept: none 
E) x-intercept: $\left( \frac { 7 } { 13 } , 0 \right)$ y-intercept: (0,7) 
A) x-intercept: $\left( - \frac { 7 } { 13 } , 0 \right)$ y-intercept: (0,13) 
B)  x-intercept: $\left( - \frac { 13 } { 7 } , 0 \right)$
Y-intercept: (0,-7) 
C) x-intercept: (-7,0) y-intercept: (0,13) 
D) x-intercept: $\left( - \frac { 13 } { 7 } , 0 \right)$ y-intercept: none 
E) x-intercept: $\left( \frac { 7 } { 13 } , 0 \right)$ y-intercept: (0,7)

Question 9

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $y = 4 x ^ { 20 } - x ^ { 10 } - 3$

Accepted Answer

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

Question 10

Assume that the graph has Origin symmetry.Select the complete graph of the equation.

Accepted Answer

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

Question 11

Assume the graph has the indicated type of symmetry.Sketch the complete graph.   symmetric with respect to the origin.

Accepted Answer

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

Question 12

Find the center and radius of the circle,and sketch its graph.$$\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$$

Accepted Answer

A) Centre $$\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$$ ,Radius $\frac { 49 } { 4 }$    
B) Centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ ,Radius $\frac { 49 } { 4 }$   
C) Centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ ,Radius $\frac { 7 } { 2 }$    
D) Centre $\left( - \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)$ ,Radius $\frac { 7 } { 4 }$    
E) Centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ ,Radius $\frac { 7 } { 2 }$    
A) Centre $$\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$$ ,Radius $\frac { 49 } { 4 }$    
B) Centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ ,Radius $\frac { 49 } { 4 }$   
C) Centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ ,Radius $\frac { 7 } { 2 }$    
D) Centre $\left( - \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right)$ ,Radius $\frac { 7 } { 4 }$    
E) Centre $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ ,Radius $\frac { 7 } { 2 }$

Question 13

Write the standard form of the equation of the circle with the given characteristics. 
Center: (6,1);Solution point: (5,9)

Accepted Answer

A)  $( x + 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 65$ 
B)  $( x - 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } - 65 = 0$ 
C)  $( x + 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + 65 = 0$ 
D)  $( x - 6 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 65$ 
E)  $( x - 1 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 65$ 
A)  $( x + 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 65$ 
B)  $( x - 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } - 65 = 0$ 
C)  $( x + 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } + 65 = 0$ 
D)  $( x - 6 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 65$ 
E)  $( x - 1 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 65$

Question 14

Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3,4), (7,8)

Accepted Answer

A)  $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
B)  $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 8$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
D)  $( x + 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 340$ 
E)  $( x - 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 340$ 
A)  $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
B)  $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 8$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
D)  $( x + 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 340$ 
E)  $( x - 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 340$

Question 15

Find the x- and y-intercepts of the graph of the equation $$y = \sqrt { - 8 x - 7 }$$ .

Accepted Answer

A) x-intercept: $\left( - \frac { 8 } { 7 } , 0 \right)$ y-intercept: none 
B) x-intercept: $$\left( - \frac { 7 } { 8 } , 0 \right)$$ y-intercept: $( 0 , - 7 )$ 
C) x-intercept: $( 7,0 )$ y-intercept: none 
D) x-intercept: $( - 8,0 )$ y-intercept: $( 0,7 )$ 
E) x-intercept: $\left( - \frac { 7 } { 8 } , 0 \right)$ y-intercept: none 
A) x-intercept: $\left( - \frac { 8 } { 7 } , 0 \right)$ y-intercept: none 
B) x-intercept: $$\left( - \frac { 7 } { 8 } , 0 \right)$$ y-intercept: $( 0 , - 7 )$ 
C) x-intercept: $( 7,0 )$ y-intercept: none 
D) x-intercept: $( - 8,0 )$ y-intercept: $( 0,7 )$ 
E) x-intercept: $\left( - \frac { 7 } { 8 } , 0 \right)$ y-intercept: none

Question 16

Write the standard form of the equation of the circle with the given characteristics. center: (-1,-5);radius: 6

Accepted Answer

A)  $( x - 1 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 36$ 
B)  $( x + 5 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 6$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 36$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 6$ 
E)  $( x + 1 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 36$ 
A)  $( x - 1 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 36$ 
B)  $( x + 5 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 6$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 36$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 6$ 
E)  $( x + 1 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 36$

Question 17

Find the center and radius of the circle $( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25$ .

Accepted Answer

A) center: (1,5),radius 5 
B) center: (5,1),radius 25 
C) center: (-5,-1),radius 5 
D) center: (-5,-1),radius 25 
E) center: (5,1),radius 5 
A) center: (1,5),radius 5 
B) center: (5,1),radius 25 
C) center: (-5,-1),radius 5 
D) center: (-5,-1),radius 25 
E) center: (5,1),radius 5

Question 18

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. 
Y = |x - 4|

Accepted Answer

A) x- intercept: (4,0) y- intercept: (0,4)
No symmetry
   
B) x- intercept: (-4,0) y- intercept: (0,4)
No symmetry
   
C) x- intercept: (4,0) y- intercept: (4,0)
No symmetry
   
D) x- intercept: (4,0) y- intercept: (0,4)
No symmetry
   
E) x- intercept: (4,0) y- intercept: (4,0)
No symmetry
   
A) x- intercept: (4,0) y- intercept: (0,4)
No symmetry
   
B) x- intercept: (-4,0) y- intercept: (0,4)
No symmetry
   
C) x- intercept: (4,0) y- intercept: (4,0)
No symmetry
   
D) x- intercept: (4,0) y- intercept: (0,4)
No symmetry
   
E) x- intercept: (4,0) y- intercept: (4,0)
No symmetry

Question 19

Graphically estimate the x- and y-intercepts of the graph. $$y = x ^ { 3 } - x$$

Accepted Answer

A) x-intercept: (±1,0), (0,0) y-intercept: (0,0) 
B) x-intercept: (1,0), (0,0) y-intercept: (0,0) 
C) x-intercept: (-1,0), (0,0) y-intercept: (0,0) 
D) x-intercept: (0,±1), (0,0) y-intercept: (0,0) 
E) x-intercept: (0,1), (0,0) y-intercept: (0,0) 
A) x-intercept: (±1,0), (0,0) y-intercept: (0,0) 
B) x-intercept: (1,0), (0,0) y-intercept: (0,0) 
C) x-intercept: (-1,0), (0,0) y-intercept: (0,0) 
D) x-intercept: (0,±1), (0,0) y-intercept: (0,0) 
E) x-intercept: (0,1), (0,0) y-intercept: (0,0)

Question 20

Find the x-intercept of the graph of the equation y = 3x + 15.

Accepted Answer

A) (0,-5) 
B) (0,15) 
C) (15,0) 
D) (0,3) 
E) (-5,0) 
A) (0,-5) 
B) (0,15) 
C) (15,0) 
D) (0,3) 
E) (-5,0)

Exam 2: Graphs of Equations

Determine which of the following point lies on the graph of the equation. Y = 3 - |x - 1|

Find the x- and y-intercepts of the graph of the equation y = 36 - 6x.

Determine which of the following point lies on the graph of the equation. y=13x3−3x2y = \frac { 1 } { 3 } x ^ { 3 } - 3 x ^ { 2 }y=31​x3−3x2

Find the graph of the equation. ? F (x)= | x - 2 |

Identify any intercepts and test for symmetry.Then sketch the graph of the equation.? y=x2+3y = x ^ { 2 } + 3y=x2+3 ?

Find the y-intercept of the graph of the equation y = 3x + 18.

Which of the following graphs are symmetric about the y-axis?

Find the x- and y-intercepts of the graph of the equation y=∣13x−7∣y = | 13 x - 7 |y=∣13x−7∣ .

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. y=4x20−x10−3y = 4 x ^ { 20 } - x ^ { 10 } - 3y=4x20−x10−3

Assume that the graph has Origin symmetry.Select the complete graph of the equation.

Assume the graph has the indicated type of symmetry.Sketch the complete graph. symmetric with respect to the origin.

Find the center and radius of the circle,and sketch its graph. (x−12)2+(y−12)2=494\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }(x−21​)2+(y−21​)2=449​

Write the standard form of the equation of the circle with the given characteristics. Center: (6,1);Solution point: (5,9)

Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3,4), (7,8)

Find the x- and y-intercepts of the graph of the equation y=−8x−7y = \sqrt { - 8 x - 7 }y=−8x−7​ .

Write the standard form of the equation of the circle with the given characteristics. center: (-1,-5);radius: 6

Find the center and radius of the circle (x−5)2+(y−1)2=25( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25(x−5)2+(y−1)2=25 .

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. Y = |x - 4|

Graphically estimate the x- and y-intercepts of the graph. y=x3−xy = x ^ { 3 } - xy=x3−x

Find the x-intercept of the graph of the equation y = 3x + 15.

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

Determine which of the following point lies on the graph of the equation. $y = \frac { 1 } { 3 } x ^ { 3 } - 3 x ^ { 2 }$

Identify any intercepts and test for symmetry.Then sketch the graph of the equation.? $y = x ^ { 2 } + 3$ ?

Find the x- and y-intercepts of the graph of the equation $y = | 13 x - 7 |$ .

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $y = 4 x ^ { 20 } - x ^ { 10 } - 3$

Find the center and radius of the circle,and sketch its graph. $\left( x - \frac { 1 } { 2 } \right) ^ { 2 } + \left( y - \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 49 } { 4 }$

Find the x- and y-intercepts of the graph of the equation $y = \sqrt { - 8 x - 7 }$ .

Find the center and radius of the circle $( x - 5 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25$ .

Graphically estimate the x- and y-intercepts of the graph. $y = x ^ { 3 } - x$ $Graphically estimate the x- and y-intercepts of the graph. y = x ^ { 3 } - x$