Question 1

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $\mathrm { y } = - 5$, through $( 7,3 )$

Accepted Answer

A)  $y = 3$ 
B)  $y = 7$ 
C)  $x = 7$ 
D)  $x = 3$ 
A)  $y = 3$ 
B)  $y = 7$ 
C)  $x = 7$ 
D)  $x = 3$

Question 2

Graph the function.
-

Accepted Answer

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

Question 3

Graph the function.
-$f(x)=(x-1)^{3}-6$

Accepted Answer

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

Question 4

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$y+x=4 ;(1,),(4,),(3,)$

Accepted Answer

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

Question 5

Find the requested function value.
-Find $( g \circ f ) ( 44 )$ when $f ( x ) = \frac { x - 2 } { 7 }$ and $g ( x ) = 8 x + 5$.

Accepted Answer

A)  $\frac { 355 } { 7 }$ 
B)  53 
C)  2142 
D)  78 
A)  $\frac { 355 } { 7 }$ 
B)  53 
C)  2142 
D)  78

Question 6

Evaluate.
-Find $( f - g ) ( - 3 )$ when $f ( x ) = 3 x ^ { 2 } - 6$ and $g ( x ) = x + 3$

Accepted Answer

A)  $- 18$ 
B)  21 
C)  27 
D)  15 
A)  $- 18$ 
B)  21 
C)  27 
D)  15

Question 7

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.
-$$f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$$

Accepted Answer

A)  Yes, no 
B)  Yes, yes 
C)  No, no 
D)  No, yes 
A)  Yes, no 
B)  Yes, yes 
C)  No, no 
D)  No, yes

Question 8

Graph the point symmetric to the given point.
-Plot the point (3, -2), then plot the point that is symmetric to (3, -2) with respect to the origin.

Accepted Answer

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

Question 9

Graph the function.
-$$y = - \frac { 1 } { 2 } ( x + 5 ) ^ { 4 } + 1$$

Accepted Answer

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

Question 10

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$2 x ^ { 2 } + 2 y ^ { 2 } - 4 x + 20 y + 2 = 0$$

Accepted Answer

A)  no; the graph is the point (-1, 5) 
B)  yes 
C)  no; the graph is nonexistent 
D)  no; the graph is the point (1, -5) 
A)  no; the graph is the point (-1, 5) 
B)  yes 
C)  no; the graph is nonexistent 
D)  no; the graph is the point (1, -5)

Question 11

Refer to the following graphs to determine an appropriate response.  
-Which one is the graph of $y = [ [ x ] ]$ ? What is the value of $y$ when $x = 1.5$ ?

Accepted Answer

A)  graph B; $2.25$ 
B)  graph D; 1 
C)  graph $C ; 1$ 
D)  graph A; $2.25$ 
A)  graph B; $2.25$ 
B)  graph D; 1 
C)  graph $C ; 1$ 
D)  graph A; $2.25$

Question 12

Solve the problem.
-Use the graphs to find the value of $( f + g ) ( 3 )$.

Accepted Answer

A)  $- 1$ 
B)  1 
C)  0 
D)  3 
A)  $- 1$ 
B)  1 
C)  0 
D)  3

Question 13

Find the requested value.
-$f ( - 7 )$ for $f ( x ) = \left\{ \begin{array} { l l } 4 x + 1 , & \text { if } x  11 \end{array} \right.$

Accepted Answer

A)  29 
B)  $- 27$ 
C)  $- 49$ 
D)  63 
A)  29 
B)  $- 27$ 
C)  $- 49$ 
D)  63

Question 14

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 8 x ^ { 2 } - 9 x , g ( x ) = x ^ { 2 } - 3 x - 54$$
Find $\left( \frac { f } { g } \right) ( x )$.

Accepted Answer

A)  $\frac { 8 x ^ { 2 } - 9 x } { x ^ { 2 } - 3 x - 54 }$ 
B)  $\frac { 8 - x } { 54 }$ 
C)  $\frac { 8 x } { x + 1 }$ 
D)  $\frac { 8 x - 9 } { - 3 }$ 
A)  $\frac { 8 x ^ { 2 } - 9 x } { x ^ { 2 } - 3 x - 54 }$ 
B)  $\frac { 8 - x } { 54 }$ 
C)  $\frac { 8 x } { x + 1 }$ 
D)  $\frac { 8 x - 9 } { - 3 }$

Question 15

For the given functions f and g , find the indicated composition.
-$$f ( x ) = - 3 x + 6 , \quad g ( x ) = 5 x + 5$$
$( g \circ f ) ( x )$

Accepted Answer

A)  $- 15 x + 21$ 
B)  $- 15 x - 25$ 
C)  $- 15 x + 35$ 
D)  $15 x + 35$ 
A)  $- 15 x + 21$ 
B)  $- 15 x - 25$ 
C)  $- 15 x + 35$ 
D)  $15 x + 35$

Question 16

Determine if the function is even, odd, or neither.
-$$f ( x ) = - 6 x ^ { 5 } - 5 x ^ { 3 }$$

Accepted Answer

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

Question 17

Find the slope of the line satisfying the given conditions.
-through $( - 9 , - 2 )$ and $( - 7 , - 2 )$

Accepted Answer

A)  2 
B)  undefined 
C)  0 
D)  $- 2$ 
A)  2 
B)  undefined 
C)  0 
D)  $- 2$

Question 18

Refer to the following graphs to determine an appropriate response.  
-Which one is the graph of $y = \sqrt { x }$ ? What is it's domain?

Accepted Answer

A)  graph B; $[ 0 , \infty )$ 
B)  graph D; $[ 0 , \infty )$ 
C)  graph $C ; \{ - 2 , - 1,0,1,2 \}$ 
D)  graph $A ; ( - \infty , \infty )$ 
A)  graph B; $[ 0 , \infty )$ 
B)  graph D; $[ 0 , \infty )$ 
C)  graph $C ; \{ - 2 , - 1,0,1,2 \}$ 
D)  graph $A ; ( - \infty , \infty )$

Question 19

Decide whether the relation defines a function.
-

Accepted Answer

A)  $\text { Not a function }$ 
B)  Function 
A)  $\text { Not a function }$ 
B)  Function

Question 20

Use the graph to solve the problem.
-What temperature was recorded at 4 p.m.?

Accepted Answer

A)  $74 ^ { \circ } \mathrm { F }$ 
B)  $77 ^ { \circ } \mathrm { F }$ 
C)  $78 ^ { \circ } \mathrm { F }$ 
D)  $76 ^ { \circ } \mathrm { F }$ 
A)  $74 ^ { \circ } \mathrm { F }$ 
B)  $77 ^ { \circ } \mathrm { F }$ 
C)  $78 ^ { \circ } \mathrm { F }$ 
D)  $76 ^ { \circ } \mathrm { F }$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $\mathrm { y } = - 5$ , through $( 7,3 )$

Graph the function. -

Graph the function. - $f(x)=(x-1)^{3}-6$ $Graph the function. - f(x)=(x-1)^{3}-6$

Graph the equation by determining the missing values needed to plot the ordered pairs. - $y+x=4 ;(1,),(4,),(3,)$

Find the requested function value. -Find $( g \circ f ) ( 44 )$ when $f ( x ) = \frac { x - 2 } { 7 }$ and $g ( x ) = 8 x + 5$ .

Evaluate. -Find $( f - g ) ( - 3 )$ when $f ( x ) = 3 x ^ { 2 } - 6$ and $g ( x ) = x + 3$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$

Graph the point symmetric to the given point. -Plot the point (3, -2), then plot the point that is symmetric to (3, -2) with respect to the origin.

Graph the function. - $y = - \frac { 1 } { 2 } ( x + 5 ) ^ { 4 } + 1$ $Graph the function. - y = - \frac { 1 } { 2 } ( x + 5 ) ^ { 4 } + 1$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $2 x ^ { 2 } + 2 y ^ { 2 } - 4 x + 20 y + 2 = 0$

Refer to the following graphs to determine an appropriate response. -Which one is the graph of $y = [ [ x ] ]$ ? What is the value of $y$ when $x = 1.5$ ?

Solve the problem. -Use the graphs to find the value of $( f + g ) ( 3 )$ .

Find the requested value. - $f ( - 7 )$ for $f ( x ) = \left\{ \begin{array} { l l } 4 x + 1 , & \text { if } x < 7 \\ 7 x , & \text { if } 7 \leq x \leq 11 \\ 7 - 8 x , & \text { if } x > 11 \end{array} \right.$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 8 x ^ { 2 } - 9 x , g ( x ) = x ^ { 2 } - 3 x - 54$ Find $\left( \frac { f } { g } \right) ( x )$ .

For the given functions f and g , find the indicated composition. - $f ( x ) = - 3 x + 6 , \quad g ( x ) = 5 x + 5$ $( g \circ f ) ( x )$

Determine if the function is even, odd, or neither. - $f ( x ) = - 6 x ^ { 5 } - 5 x ^ { 3 }$

Find the slope of the line satisfying the given conditions. -through $( - 9 , - 2 )$ and $( - 7 , - 2 )$

Refer to the following graphs to determine an appropriate response. $Refer to the following graphs to determine an appropriate response. -Which one is the graph of y = \sqrt { x } ? What is it's domain?$ -Which one is the graph of $y = \sqrt { x }$ ? What is it's domain?

Decide whether the relation defines a function. -

Use the graph to solve the problem. -What temperature was recorded at 4 p.m.?

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

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y=−5\mathrm { y } = - 5y=−5 , through (7,3)( 7,3 )(7,3)

Graph the function. -

Graph the function. - f(x)=(x−1)3−6f(x)=(x-1)^{3}-6f(x)=(x−1)3−6

Graph the equation by determining the missing values needed to plot the ordered pairs. - y+x=4;(1,),(4,),(3,)y+x=4 ;(1,),(4,),(3,)y+x=4;(1,),(4,),(3,)

Find the requested function value. -Find (g∘f)(44)( g \circ f ) ( 44 )(g∘f)(44) when f(x)=x−27f ( x ) = \frac { x - 2 } { 7 }f(x)=7x−2​ and g(x)=8x+5g ( x ) = 8 x + 5g(x)=8x+5 .

Evaluate. -Find (f−g)(−3)( f - g ) ( - 3 )(f−g)(−3) when f(x)=3x2−6f ( x ) = 3 x ^ { 2 } - 6f(x)=3x2−6 and g(x)=x+3g ( x ) = x + 3g(x)=x+3

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - f(x)=x−75,g(x)=x5+7f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7f(x)=5x−7​,g(x)=x5+7

Graph the point symmetric to the given point. -Plot the point (3, -2), then plot the point that is symmetric to (3, -2) with respect to the origin.

Graph the function. - y=−12(x+5)4+1y = - \frac { 1 } { 2 } ( x + 5 ) ^ { 4 } + 1y=−21​(x+5)4+1

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - 2x2+2y2−4x+20y+2=02 x ^ { 2 } + 2 y ^ { 2 } - 4 x + 20 y + 2 = 02x2+2y2−4x+20y+2=0

Refer to the following graphs to determine an appropriate response. -Which one is the graph of y=[[x]]y = [ [ x ] ]y=[[x]] ? What is the value of yyy when x=1.5x = 1.5x=1.5 ?

Solve the problem. -Use the graphs to find the value of (f+g)(3)( f + g ) ( 3 )(f+g)(3) .

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=8x2−9x,g(x)=x2−3x−54f ( x ) = 8 x ^ { 2 } - 9 x , g ( x ) = x ^ { 2 } - 3 x - 54f(x)=8x2−9x,g(x)=x2−3x−54 Find (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) .

For the given functions f and g , find the indicated composition. - f(x)=−3x+6,g(x)=5x+5f ( x ) = - 3 x + 6 , \quad g ( x ) = 5 x + 5f(x)=−3x+6,g(x)=5x+5 (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Determine if the function is even, odd, or neither. - f(x)=−6x5−5x3f ( x ) = - 6 x ^ { 5 } - 5 x ^ { 3 }f(x)=−6x5−5x3

Find the slope of the line satisfying the given conditions. -through (−9,−2)( - 9 , - 2 )(−9,−2) and (−7,−2)( - 7 , - 2 )(−7,−2)

Refer to the following graphs to determine an appropriate response. -Which one is the graph of y=xy = \sqrt { x }y=x​ ? What is it's domain?

Decide whether the relation defines a function. -

Use the graph to solve the problem. -What temperature was recorded at 4 p.m.?

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

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $\mathrm { y } = - 5$ , through $( 7,3 )$

Graph the function. - $f(x)=(x-1)^{3}-6$ $Graph the function. - f(x)=(x-1)^{3}-6$

Graph the equation by determining the missing values needed to plot the ordered pairs. - $y+x=4 ;(1,),(4,),(3,)$

Find the requested function value. -Find $( g \circ f ) ( 44 )$ when $f ( x ) = \frac { x - 2 } { 7 }$ and $g ( x ) = 8 x + 5$ .

Evaluate. -Find $( f - g ) ( - 3 )$ when $f ( x ) = 3 x ^ { 2 } - 6$ and $g ( x ) = x + 3$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = \sqrt [ 5 ] { x - 7 } , g ( x ) = x ^ { 5 } + 7$

Graph the function. - $y = - \frac { 1 } { 2 } ( x + 5 ) ^ { 4 } + 1$ $Graph the function. - y = - \frac { 1 } { 2 } ( x + 5 ) ^ { 4 } + 1$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $2 x ^ { 2 } + 2 y ^ { 2 } - 4 x + 20 y + 2 = 0$

Refer to the following graphs to determine an appropriate response. -Which one is the graph of $y = [ [ x ] ]$ ? What is the value of $y$ when $x = 1.5$ ?

Solve the problem. -Use the graphs to find the value of $( f + g ) ( 3 )$ .

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 8 x ^ { 2 } - 9 x , g ( x ) = x ^ { 2 } - 3 x - 54$ Find $\left( \frac { f } { g } \right) ( x )$ .

For the given functions f and g , find the indicated composition. - $f ( x ) = - 3 x + 6 , \quad g ( x ) = 5 x + 5$ $( g \circ f ) ( x )$

Determine if the function is even, odd, or neither. - $f ( x ) = - 6 x ^ { 5 } - 5 x ^ { 3 }$

Find the slope of the line satisfying the given conditions. -through $( - 9 , - 2 )$ and $( - 7 , - 2 )$

Refer to the following graphs to determine an appropriate response. $Refer to the following graphs to determine an appropriate response. -Which one is the graph of y = \sqrt { x } ? What is it's domain?$ -Which one is the graph of $y = \sqrt { x }$ ? What is it's domain?