Question 1

Provide an appropriate response.
-If the point (a, b) is in the fourth quadrant, in what quadrant is ( $( - \mathrm { a } , - \mathrm { b } )$

Accepted Answer

A)  II 
B)  IV 
C)  I 
D)  III 
A)  II 
B)  IV 
C)  I 
D)  III

Question 2

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $\{ - 1 \}$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $\{ - 1 \}$; range: $( - \infty , \infty )$ 
A)  domain: $( - \infty , \infty )$; range: $\{ - 1 \}$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $\{ - 1 \}$; range: $( - \infty , \infty )$

Question 3

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } + 6 x - 18 y + 90 = 0$$

Accepted Answer

A)  no; the graph is the point $( 3 , - 9 )$ 
B)  no; the graph is the point $( - 3,9 )$ 
C)  no; the graph is nonexistent 
D)  yes 
A)  no; the graph is the point $( 3 , - 9 )$ 
B)  no; the graph is the point $( - 3,9 )$ 
C)  no; the graph is nonexistent 
D)  yes

Question 4

Find the slope of the line satisfying the given conditions.
-vertical, through $( 3 , - 8 )$

Accepted Answer

A)  -1 
B)  1 
C)  0 
D)  undefined 
A)  -1 
B)  1 
C)  0 
D)  undefined

Question 5

Choose the value which could represent the slope of the line. Assume that the scale on the x-axis is the same as the scale
on the y-axis.
-

Accepted Answer

A)  undefined 
B)  1 
C)  0 
D)  $\frac { 3 } { 2 }$ 
A)  undefined 
B)  1 
C)  0 
D)  $\frac { 3 } { 2 }$

Question 6

Write an equation for the line described. Write the equation in the form specified.
-parallel to $2 x + 7 y = 65$, through $( 8,4 )$; slope-intercept form

Accepted Answer

A)  $y = \frac { 2 } { 7 } x - \frac { 44 } { 7 }$ 
B)  $y = - \frac { 2 } { 7 } x + \frac { 44 } { 7 }$ 
C)  $y = - \frac { 8 } { 7 } x + \frac { 65 } { 7 }$ 
D)  $y = - \frac { 7 } { 2 } x + 2$ 
A)  $y = \frac { 2 } { 7 } x - \frac { 44 } { 7 }$ 
B)  $y = - \frac { 2 } { 7 } x + \frac { 44 } { 7 }$ 
C)  $y = - \frac { 8 } { 7 } x + \frac { 65 } { 7 }$ 
D)  $y = - \frac { 7 } { 2 } x + 2$

Question 7

Determine whether the three points are collinear.
-$$( 0 , - 9 ) , ( 7 , - 7 ) , ( - 7 , - 11 )$$

Accepted Answer

A) True 
 B)False

Question 8

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$g(x)=x+1$

Accepted Answer

A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $ D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $ D = ( - \infty , \infty ) , R = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$

Question 9

Find the requested value.
-$f(x)=\left\{\begin{array}{ll}
4, & \text { if } x>1 \
-4, & \text { if } x \leq 1
\end{array}\right.$

Accepted Answer

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

Question 10

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ .
-$f(x)=5 x^{2}$

Accepted Answer

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

Question 11

Determine if the function is even, odd, or neither.
-$f ( x ) = - 8 x ^ { 5 } + 4 x ^ { 3 }$

Accepted Answer

A)  Neither 
B)  Even 
C)  Odd 
A)  Neither 
B)  Even 
C)  Odd

Question 12

Match the description with the correct symbolic expression.
-a function that is not linear

Accepted Answer

A)  $f ( x ) = 7 x + 2$ 
B)  $f ( x ) = - 4$ 
C)  $f ( x ) = - 6 x + 7$ 
D)  $f ( x ) = x ^ { 2 } - 6$ 
A)  $f ( x ) = 7 x + 2$ 
B)  $f ( x ) = - 4$ 
C)  $f ( x ) = - 6 x + 7$ 
D)  $f ( x ) = x ^ { 2 } - 6$

Question 13

Find the specified domain.
-Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \frac { 5 } { x - 3 }$ and $g ( x ) = 11 - x$

Accepted Answer

A)  $( - \infty , 11 ) \cup ( 11 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $( - \infty , 3 ) \cup ( 3,11 ) \cup ( 11 , \infty )$ 
D)  $( - \infty , - 11 ) \cup ( - 11 , - 3 ) \cup ( - 3 , \infty )$ 
A)  $( - \infty , 11 ) \cup ( 11 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
C)  $( - \infty , 3 ) \cup ( 3,11 ) \cup ( 11 , \infty )$ 
D)  $( - \infty , - 11 ) \cup ( - 11 , - 3 ) \cup ( - 3 , \infty )$

Question 14

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 6 x + 4 } , g ( x ) = \frac { 1 } { x }$$
Find $( f - g ) ( x )$

Accepted Answer

A)  $\sqrt { 6 x + 4 - \frac { 1 } { x } }$ 
B)  $\frac { 1 } { \sqrt { 6 x + 4 } - x }$ 
C)  $\sqrt { 6 x + 4 } - \frac { 1 } { x }$ 
D)  $\frac { 1 } { x } - \sqrt { 6 x + 4 }$ 
A)  $\sqrt { 6 x + 4 - \frac { 1 } { x } }$ 
B)  $\frac { 1 } { \sqrt { 6 x + 4 } - x }$ 
C)  $\sqrt { 6 x + 4 } - \frac { 1 } { x }$ 
D)  $\frac { 1 } { x } - \sqrt { 6 x + 4 }$

Question 15

Decide whether the relation defines a function.
-$$\{ ( 1 , - 4 ) , ( 2 , - 2 ) , ( 6,7 ) , ( 8 , - 7 ) , ( 11 , - 1 ) \}$$

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 16

Find the slope of the line and sketch the graph.
-$y=3 x$

Accepted Answer

A)  $m = \frac { 1 } { 3 }$
  
B)  $m = - 3$
  
C)  $m = 3$
  
D)  $m = 0$
  
A)  $m = \frac { 1 } { 3 }$
  
B)  $m = - 3$
  
C)  $m = 3$
  
D)  $m = 0$

Question 17

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x).
-$$9 x - 5 y = 7$$

Accepted Answer

A)  $f ( x ) = \frac { 5 } { 9 } x + \frac { 7 } { 9 }$ 
B)  $f ( x ) = 9 x - 7$ 
C)  $f ( x ) = \frac { 9 } { 5 } x + \frac { 7 } { 5 }$ 
D)  $f ( x ) = \frac { 9 } { 5 } x - \frac { 7 } { 5 }$ 
A)  $f ( x ) = \frac { 5 } { 9 } x + \frac { 7 } { 9 }$ 
B)  $f ( x ) = 9 x - 7$ 
C)  $f ( x ) = \frac { 9 } { 5 } x + \frac { 7 } { 5 }$ 
D)  $f ( x ) = \frac { 9 } { 5 } x - \frac { 7 } { 5 }$

Question 18

Graph the circle.
-$(x-5)^{2}+y^{2}=4$

Accepted Answer

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

Question 19

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $y = 2$, through $( 3,4 )$

Accepted Answer

A)  $x = 4$ 
B)  $y = 3$ 
C)  $x = 3$ 
D)  $y = 4$ 
A)  $x = 4$ 
B)  $y = 3$ 
C)  $x = 3$ 
D)  $y = 4$

Question 20

Graph the line and give the domain and the range.
-$x=-5$

Accepted Answer

A)  $D = \{ - 5 \} , R = ( - \infty , \infty )$
  
B)  $D = \{ - 5 \} , \quad R = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ - 5 \}$
  
D)  $D = ( - \infty , \infty ) , R = \{ - 5 \}$
  
A)  $D = \{ - 5 \} , R = ( - \infty , \infty )$
  
B)  $D = \{ - 5 \} , \quad R = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ - 5 \}$
  
D)  $D = ( - \infty , \infty ) , R = \{ - 5 \}$

Provide an appropriate response. -If the point (a, b) is in the fourth quadrant, in what quadrant is ( $( - \mathrm { a } , - \mathrm { b } )$

Give the domain and range of the relation. -

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 6 x - 18 y + 90 = 0$

Find the slope of the line satisfying the given conditions. -vertical, through $( 3 , - 8 )$

Choose the value which could represent the slope of the line. Assume that the scale on the x-axis is the same as the scale on the y-axis. -

Write an equation for the line described. Write the equation in the form specified. -parallel to $2 x + 7 y = 65$ , through $( 8,4 )$ ; slope-intercept form

Determine whether the three points are collinear. - $( 0 , - 9 ) , ( 7 , - 7 ) , ( - 7 , - 11 )$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $g(x)=x+1$

Find the requested value. - $f(x)=\left\{\begin{array}{ll}4, & \text { if } x>1 \\-4, & \text { if } x \leq 1\end{array}\right.$ $Find the requested value. - f(x)=\left\{\begin{array}{ll} 4, & \text { if } x>1 \\ -4, & \text { if } x \leq 1 \end{array}\right.$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=5 x^{2}$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=5 x^{2}$

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 5 } + 4 x ^ { 3 }$

Match the description with the correct symbolic expression. -a function that is not linear

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \frac { 5 } { x - 3 }$ and $g ( x ) = 11 - x$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 6 x + 4 } , g ( x ) = \frac { 1 } { x }$ Find $( f - g ) ( x )$

Decide whether the relation defines a function. - $\{ ( 1 , - 4 ) , ( 2 , - 2 ) , ( 6,7 ) , ( 8 , - 7 ) , ( 11 , - 1 ) \}$

Find the slope of the line and sketch the graph. - $y=3 x$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $9 x - 5 y = 7$

Graph the circle. - $(x-5)^{2}+y^{2}=4$ $Graph the circle. - (x-5)^{2}+y^{2}=4$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $y = 2$ , through $( 3,4 )$

Graph the line and give the domain and the range. - $x=-5$

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 3: Graphs and Functions

Provide an appropriate response. -If the point (a, b) is in the fourth quadrant, in what quadrant is ( (−a,−b)( - \mathrm { a } , - \mathrm { b } )(−a,−b)

Give the domain and range of the relation. -

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2+6x−18y+90=0x ^ { 2 } + y ^ { 2 } + 6 x - 18 y + 90 = 0x2+y2+6x−18y+90=0

Find the slope of the line satisfying the given conditions. -vertical, through (3,−8)( 3 , - 8 )(3,−8)

Choose the value which could represent the slope of the line. Assume that the scale on the x-axis is the same as the scale on the y-axis. -

Write an equation for the line described. Write the equation in the form specified. -parallel to 2x+7y=652 x + 7 y = 652x+7y=65 , through (8,4)( 8,4 )(8,4) ; slope-intercept form

Determine whether the three points are collinear. - (0,−9),(7,−7),(−7,−11)( 0 , - 9 ) , ( 7 , - 7 ) , ( - 7 , - 11 )(0,−9),(7,−7),(−7,−11)

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - g(x)=x+1g(x)=x+1g(x)=x+1

Find the requested value. - f(x)={4, if x>1−4, if x≤1f(x)=\left\{\begin{array}{ll}4, & \text { if } x>1 \\-4, & \text { if } x \leq 1\end{array}\right.f(x)={4,−4,​ if x>1 if x≤1​

Describe how the graph of the equation relates to the graph of y y=x3y = \sqrt [ 3 ] { x }y=3x​ . - f(x)=5x2f(x)=5 x^{2}f(x)=5x2

Determine if the function is even, odd, or neither. - f(x)=−8x5+4x3f ( x ) = - 8 x ^ { 5 } + 4 x ^ { 3 }f(x)=−8x5+4x3

Match the description with the correct symbolic expression. -a function that is not linear

Find the specified domain. -Find the domain of (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) when f(x)=5x−3f ( x ) = \frac { 5 } { x - 3 }f(x)=x−35​ and g(x)=11−xg ( x ) = 11 - xg(x)=11−x

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=6x+4,g(x)=1xf ( x ) = \sqrt { 6 x + 4 } , g ( x ) = \frac { 1 } { x }f(x)=6x+4​,g(x)=x1​ Find (f−g)(x)( f - g ) ( x )(f−g)(x)

Decide whether the relation defines a function. - {(1,−4),(2,−2),(6,7),(8,−7),(11,−1)}\{ ( 1 , - 4 ) , ( 2 , - 2 ) , ( 6,7 ) , ( 8 , - 7 ) , ( 11 , - 1 ) \}{(1,−4),(2,−2),(6,7),(8,−7),(11,−1)}

Find the slope of the line and sketch the graph. - y=3xy=3 xy=3x

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - 9x−5y=79 x - 5 y = 79x−5y=7

Graph the circle. - (x−5)2+y2=4(x-5)^{2}+y^{2}=4(x−5)2+y2=4

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y=2y = 2y=2 , through (3,4)( 3,4 )(3,4)

Graph the line and give the domain and the range. - x=−5x=-5x=−5

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Provide an appropriate response. -If the point (a, b) is in the fourth quadrant, in what quadrant is ( $( - \mathrm { a } , - \mathrm { b } )$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 6 x - 18 y + 90 = 0$

Find the slope of the line satisfying the given conditions. -vertical, through $( 3 , - 8 )$

Write an equation for the line described. Write the equation in the form specified. -parallel to $2 x + 7 y = 65$ , through $( 8,4 )$ ; slope-intercept form

Determine whether the three points are collinear. - $( 0 , - 9 ) , ( 7 , - 7 ) , ( - 7 , - 11 )$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $g(x)=x+1$

Find the requested value. - $f(x)=\left\{\begin{array}{ll}4, & \text { if } x>1 \\-4, & \text { if } x \leq 1\end{array}\right.$ $Find the requested value. - f(x)=\left\{\begin{array}{ll} 4, & \text { if } x>1 \\ -4, & \text { if } x \leq 1 \end{array}\right.$

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ . - $f(x)=5 x^{2}$ $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } . - f(x)=5 x^{2}$

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 5 } + 4 x ^ { 3 }$

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = \frac { 5 } { x - 3 }$ and $g ( x ) = 11 - x$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 6 x + 4 } , g ( x ) = \frac { 1 } { x }$ Find $( f - g ) ( x )$

Decide whether the relation defines a function. - $\{ ( 1 , - 4 ) , ( 2 , - 2 ) , ( 6,7 ) , ( 8 , - 7 ) , ( 11 , - 1 ) \}$

Find the slope of the line and sketch the graph. - $y=3 x$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $9 x - 5 y = 7$

Graph the circle. - $(x-5)^{2}+y^{2}=4$ $Graph the circle. - (x-5)^{2}+y^{2}=4$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $y = 2$ , through $( 3,4 )$

Graph the line and give the domain and the range. - $x=-5$