Question 1

For the given functions f and g , find the indicated composition.
-$f ( x ) = \sqrt { x + 8 } , \quad g ( x ) = 8 x - 12$ $( f \circ g ) ( x )$

Accepted Answer

A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x + 8 } - 12$ 
A)  $8 \sqrt { x - 4 }$ 
B)  $2 \sqrt { 2 x - 1 }$ 
C)  $2 \sqrt { 2 x + 1 }$ 
D)  $8 \sqrt { x + 8 } - 12$

Question 2

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 3

Find the slope of the line satisfying the given conditions.
-through $( 7 , - 9 )$ and $( - 7,9 )$

Accepted Answer

A)  $\frac { 9 } { 7 }$ 
B)  $- \frac { 7 } { 9 }$ 
C)  $\frac { 7 } { 9 }$ 
D)  $- \frac { 9 } { 7 }$ 
A)  $\frac { 9 } { 7 }$ 
B)  $- \frac { 7 } { 9 }$ 
C)  $\frac { 7 } { 9 }$ 
D)  $- \frac { 9 } { 7 }$

Question 4

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 4 x - 25 }$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $( 3 x + 5 ) ( 2 x - 5 )$ 
B)  $( \sqrt { 3 x + 5 } ) ( \sqrt { 4 x - 25 } )$ 
C)  $( 2 x - 5 ) ( \sqrt { 3 x + 5 } )$ 
D)  $( 3 x + 5 ) ( 4 x - 25 )$ 
A)  $( 3 x + 5 ) ( 2 x - 5 )$ 
B)  $( \sqrt { 3 x + 5 } ) ( \sqrt { 4 x - 25 } )$ 
C)  $( 2 x - 5 ) ( \sqrt { 3 x + 5 } )$ 
D)  $( 3 x + 5 ) ( 4 x - 25 )$

Question 5

Graph the point symmetric to the given point.
-Plot the point (9, 0), then plot the point that is symmetric to (9, 0) with respect to the y-axis.

Accepted Answer

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

Question 6

Match the description with the correct symbolic expression.
-a line with a negative slope

Accepted Answer

A)  f(x) = 2x -2 
B)  x = -2 
C) y = -5 
D) 2x + 7y = -5 
A)  f(x) = 2x -2 
B)  x = -2 
C) y = -5 
D) 2x + 7y = -5

Question 7

Find the requested value.
-Using the given tables, find ( $g \circ f ) ( 3 )$

Accepted Answer

A)  13 
B)  7 
C)  3 
D)  5 
A)  13 
B)  7 
C)  3 
D)  5

Question 8

Graph the point symmetric to the given point.
-Plot the point (0, -8), then plot the point that is symmetric to (0, -8) with respect to the y-axis.

Accepted Answer

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

Question 9

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 10

Find the slope of the line satisfying the given conditions.
-through $( - 9 , - 2 )$ and $( - 3 , - 4 )$

Accepted Answer

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

Question 11

Graph the circle.
-$(x-3)^{2}+y^{2}=4$

Accepted Answer

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

Question 12

Match the description with the correct symbolic expression.
-a linear function whose graph passes through the origin

Accepted Answer

A)  y = -4x 
B)  8x - 5y = 8 
C)  f(x) = 3 
D) x = 3 
A)  y = -4x 
B)  8x - 5y = 8 
C)  f(x) = 3 
D) x = 3

Question 13

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none
of these.
-$y = - 8 x ^ { 4 } - 4 x - 7$

Accepted Answer

A)  $y$-axis only 
B)  x-axis only 
C)  origin only 
D)  none of these 
A)  $y$-axis only 
B)  x-axis only 
C)  origin only 
D)  none of these

Question 14

Graph the function.
-

Accepted Answer

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

Question 15

Describe how the graph of the equation relates to the graph of y = x2.
-$$f ( x ) = - ( x + 7 ) ^ { 2 }$$

Accepted Answer

A)  a translation 7 units to the left and a reflection across the x-axis 
B)  a translation 7 units to the right and a reflection across the y-axis 
C)  a translation 7 units to the right and a reflection across the x-axis 
D)  a translation 7 units up and a reflection across the x-axis 
A)  a translation 7 units to the left and a reflection across the x-axis 
B)  a translation 7 units to the right and a reflection across the y-axis 
C)  a translation 7 units to the right and a reflection across the x-axis 
D)  a translation 7 units up and a reflection across the x-axis

Question 16

Determine whether the three points are collinear.
-(10, 13), (6, 8), (14, 18)

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 17

Give the domain and range of the relation.
-Annual New Telemarketing Companies

Accepted Answer

A)  None of these 
B)  domain: $\{$ Year $\}$; range: $\{$ Number $\}$ 
C)  domain: $\{ 56,112,178,187,318 \}$; range: $\{ 1995,1996,1997,1998,1999 \}$ 
D)  domain: $\{ 1995,1996,1997,1998,1999 \}$; range: $\{ 56,112,178,187,318 \}$ 
A)  None of these 
B)  domain: $\{$ Year $\}$; range: $\{$ Number $\}$ 
C)  domain: $\{ 56,112,178,187,318 \}$; range: $\{ 1995,1996,1997,1998,1999 \}$ 
D)  domain: $\{ 1995,1996,1997,1998,1999 \}$; range: $\{ 56,112,178,187,318 \}$

Question 18

Give the domain and range of the relation.
-$$y = 6 x + 1$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $[ 1 , \infty )$ 
A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $[ 1 , \infty )$

Question 19

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( 9 \sqrt { 7 } , \sqrt { 11 } ) , \mathrm { Q } ( - \sqrt { 7 } , 4 \sqrt { 11 } )$

Accepted Answer

A)  $\left( 5 \sqrt { 7 } , \frac { \sqrt { 11 } } { 2 } \right)$ 
B)  $\left( 4 \sqrt { 14 } , - \frac { \sqrt { 33 } } { 2 } \right)$ 
C)  $\left( 4 \sqrt { 7 } , \frac { 5 \sqrt { 11 } } { 2 } \right)$ 
D)  $( 4 \sqrt { 7 } , 5 \sqrt { 11 } )$ 
A)  $\left( 5 \sqrt { 7 } , \frac { \sqrt { 11 } } { 2 } \right)$ 
B)  $\left( 4 \sqrt { 14 } , - \frac { \sqrt { 33 } } { 2 } \right)$ 
C)  $\left( 4 \sqrt { 7 } , \frac { 5 \sqrt { 11 } } { 2 } \right)$ 
D)  $( 4 \sqrt { 7 } , 5 \sqrt { 11 } )$

Question 20

Graph the function.
-$y=|x+4|+2$

Accepted Answer

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

For the given functions f and g , find the indicated composition. - $f ( x ) = \sqrt { x + 8 } , \quad g ( x ) = 8 x - 12$ $( f \circ g ) ( x )$

Decide whether the relation defines a function. -

Find the slope of the line satisfying the given conditions. -through $( 7 , - 9 )$ and $( - 7,9 )$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 4 x - 25 }$ Find $( f g ) ( x )$ .

Graph the point symmetric to the given point. -Plot the point (9, 0), then plot the point that is symmetric to (9, 0) with respect to the y-axis.

Match the description with the correct symbolic expression. -a line with a negative slope

Find the requested value. -Using the given tables, find ( $g \circ f ) ( 3 )$ $Find the requested value. -Using the given tables, find ( g \circ f ) ( 3 )$

Graph the point symmetric to the given point. -Plot the point (0, -8), then plot the point that is symmetric to (0, -8) with respect to the y-axis.

Decide whether the relation defines a function. -

Find the slope of the line satisfying the given conditions. -through $( - 9 , - 2 )$ and $( - 3 , - 4 )$

Graph the circle. - $(x-3)^{2}+y^{2}=4$ $Graph the circle. - (x-3)^{2}+y^{2}=4$

Match the description with the correct symbolic expression. -a linear function whose graph passes through the origin

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - $y = - 8 x ^ { 4 } - 4 x - 7$

Graph the function. -

Describe how the graph of the equation relates to the graph of y = x2. - $f ( x ) = - ( x + 7 ) ^ { 2 }$

Determine whether the three points are collinear. -(10, 13), (6, 8), (14, 18)

Give the domain and range of the relation. -Annual New Telemarketing Companies

Give the domain and range of the relation. - $y = 6 x + 1$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 9 \sqrt { 7 } , \sqrt { 11 } ) , \mathrm { Q } ( - \sqrt { 7 } , 4 \sqrt { 11 } )$

Graph the function. - $y=|x+4|+2$

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

For the given functions f and g , find the indicated composition. - f(x)=x+8,g(x)=8x−12f ( x ) = \sqrt { x + 8 } , \quad g ( x ) = 8 x - 12f(x)=x+8​,g(x)=8x−12 (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Decide whether the relation defines a function. -

Find the slope of the line satisfying the given conditions. -through (7,−9)( 7 , - 9 )(7,−9) and (−7,9)( - 7,9 )(−7,9)

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=3x+5,g(x)=4x−25f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 4 x - 25 }f(x)=3x+5​,g(x)=4x−25​ Find (fg)(x)( f g ) ( x )(fg)(x) .

Graph the point symmetric to the given point. -Plot the point (9, 0), then plot the point that is symmetric to (9, 0) with respect to the y-axis.

Match the description with the correct symbolic expression. -a line with a negative slope

Find the requested value. -Using the given tables, find ( g∘f)(3)g \circ f ) ( 3 )g∘f)(3)

Graph the point symmetric to the given point. -Plot the point (0, -8), then plot the point that is symmetric to (0, -8) with respect to the y-axis.

Decide whether the relation defines a function. -

Find the slope of the line satisfying the given conditions. -through (−9,−2)( - 9 , - 2 )(−9,−2) and (−3,−4)( - 3 , - 4 )(−3,−4)

Graph the circle. - (x−3)2+y2=4(x-3)^{2}+y^{2}=4(x−3)2+y2=4

Match the description with the correct symbolic expression. -a linear function whose graph passes through the origin

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - y=−8x4−4x−7y = - 8 x ^ { 4 } - 4 x - 7y=−8x4−4x−7

Graph the function. -

Describe how the graph of the equation relates to the graph of y = x2. - f(x)=−(x+7)2f ( x ) = - ( x + 7 ) ^ { 2 }f(x)=−(x+7)2

Determine whether the three points are collinear. -(10, 13), (6, 8), (14, 18)

Give the domain and range of the relation. -Annual New Telemarketing Companies

Give the domain and range of the relation. - y=6x+1y = 6 x + 1y=6x+1

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(97,11),Q(−7,411)\mathrm { P } ( 9 \sqrt { 7 } , \sqrt { 11 } ) , \mathrm { Q } ( - \sqrt { 7 } , 4 \sqrt { 11 } )P(97​,11​),Q(−7​,411​)

Graph the function. - y=∣x+4∣+2y=|x+4|+2y=∣x+4∣+2

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

For the given functions f and g , find the indicated composition. - $f ( x ) = \sqrt { x + 8 } , \quad g ( x ) = 8 x - 12$ $( f \circ g ) ( x )$

Find the slope of the line satisfying the given conditions. -through $( 7 , - 9 )$ and $( - 7,9 )$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 3 x + 5 } , g ( x ) = \sqrt { 4 x - 25 }$ Find $( f g ) ( x )$ .

Find the requested value. -Using the given tables, find ( $g \circ f ) ( 3 )$ $Find the requested value. -Using the given tables, find ( g \circ f ) ( 3 )$

Find the slope of the line satisfying the given conditions. -through $( - 9 , - 2 )$ and $( - 3 , - 4 )$

Graph the circle. - $(x-3)^{2}+y^{2}=4$ $Graph the circle. - (x-3)^{2}+y^{2}=4$

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - $y = - 8 x ^ { 4 } - 4 x - 7$

Describe how the graph of the equation relates to the graph of y = x2. - $f ( x ) = - ( x + 7 ) ^ { 2 }$

Give the domain and range of the relation. - $y = 6 x + 1$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 9 \sqrt { 7 } , \sqrt { 11 } ) , \mathrm { Q } ( - \sqrt { 7 } , 4 \sqrt { 11 } )$

Graph the function. - $y=|x+4|+2$