Question 1

Describe the transformations and give the equation for the graph.
-

Accepted Answer

A)  It is the graph of $f ( x ) = | x |$ translated 9 units to the right and 4 units down. The equation is $y = | x + 9 | + 4$ 
B)  It is the graph of $\mathrm { f } ( \mathrm { x } ) = | \mathrm { x } |$ translated 9 units to the right and 4 units down. The equation is $y = | x - 9 | - 4$ 
C)  It is the graph of $f ( x ) = | x |$ translated 9 units to the right and 4 units down. The equation is $y = | x - 9 | + 4$ 
D)  It is the graph of $f ( x ) = | x |$ translated 9 units to the right and 4 units down. The equation is $y = | x + 9 | - 4$ 
A)  It is the graph of $f ( x ) = | x |$ translated 9 units to the right and 4 units down. The equation is $y = | x + 9 | + 4$ 
B)  It is the graph of $\mathrm { f } ( \mathrm { x } ) = | \mathrm { x } |$ translated 9 units to the right and 4 units down. The equation is $y = | x - 9 | - 4$ 
C)  It is the graph of $f ( x ) = | x |$ translated 9 units to the right and 4 units down. The equation is $y = | x - 9 | + 4$ 
D)  It is the graph of $f ( x ) = | x |$ translated 9 units to the right and 4 units down. The equation is $y = | x + 9 | - 4$

Question 2

Graph the function.
-$$f ( x ) = \frac { 1 } { 2 } \sqrt { - x }$$

Accepted Answer

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

Question 3

Solve the problem.
-A deep sea diving bell is being lowered at a constant rate. After 11 minutes, the bell is at a depth of 500 ft. After 40 minutes the bell is at a depth of 1800 ft. What is the average rate of change of
Depth? Round to one decimal place.

Accepted Answer

A)  0.02 ft per minute 
B)  32.5 ft per minute 
C)  45.0 ft per minute 
D)  44.8 ft per minute 
A)  0.02 ft per minute 
B)  32.5 ft per minute 
C)  45.0 ft per minute 
D)  44.8 ft per minute

Question 4

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)  $- 1$ 
B)  $- 5$ 
C)  1 
D)  5 
A)  $- 1$ 
B)  $- 5$ 
C)  1 
D)  5

Question 5

Find the average rate of change illustrated in the graph.
-

Accepted Answer

A)  $2.5$ miles per hour 
B)  5 miles per hour 
C)  $0.2$ miles per hour 
D)  25 miles per hour 
A)  $2.5$ miles per hour 
B)  5 miles per hour 
C)  $0.2$ miles per hour 
D)  25 miles per hour

Question 6

Find the requested function value.
-Find $( g \circ f ) ( - 9 )$ when $f ( x ) = 4 x + 5$ and $g ( x ) = - 5 x ^ { 2 } + 5 x - 6$

Accepted Answer

A)  $- 6$ 
B)  - 1819 
C)  $- 19$ 
D)  $- 4966$ 
A)  $- 6$ 
B)  - 1819 
C)  $- 19$ 
D)  $- 4966$

Question 7

Solve the problem.
-The graph shows an idealized linear relationship for the average monthly payment to retirees from 1995 to 1999. Use the midpoint formula to estimate the average payment in 1997. Average Monthly Payment to Retirees

Accepted Answer

A)  $\$ 44$ 
B)  $\$ 496$ 
C)  $\$ 540$ 
D)  $\$ 500$ 
A)  $\$ 44$ 
B)  $\$ 496$ 
C)  $\$ 540$ 
D)  $\$ 500$

Question 8

Find the requested function value.
-Find $( f \circ g ) ( 9 )$ when $f ( x ) = 8 x - 5$ and $g ( x ) = 3 x ^ { 2 } - 5 x + 9$.

Accepted Answer

A)  13,141 
B)  $- 125$ 
C)  1651 
D)  $- 77$ 
A)  13,141 
B)  $- 125$ 
C)  1651 
D)  $- 77$

Question 9

Solve the problem.
-The table lists how financial aid income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the financial aid cutoff for 1985.

Accepted Answer

A)  $\$ 36,000$ 
B)  $\$ 18,000$ 
C)  $\$ 57,000$ 
D)  $\$ 21,000$ 
A)  $\$ 36,000$ 
B)  $\$ 18,000$ 
C)  $\$ 57,000$ 
D)  $\$ 21,000$

Question 10

Give the domain and range of the relation.
-$$x y = - 2$$

Accepted Answer

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

Question 11

Solve the problem.
-

Accepted Answer

A)  $y = - \frac { 1 } { 2 } x ^ { 2 }$ 
B)  $y = - 2 x ^ { 2 }$ 
C)  $y = 2 x ^ { 2 }$ 
D)  $y = - x ^ { 2 }$ 
A)  $y = - \frac { 1 } { 2 } x ^ { 2 }$ 
B)  $y = - 2 x ^ { 2 }$ 
C)  $y = 2 x ^ { 2 }$ 
D)  $y = - x ^ { 2 }$

Question 12

Evaluate.
-Find (f + g)(-3) when f(x) = x - 5 and g(x) = x + 3.

Accepted Answer

A)  -4 
B) -8 
C) -14 
D)  2 
A)  -4 
B) -8 
C) -14 
D)  2

Question 13

Solve the problem.
-Select the equation that describes the graph shown.

Accepted Answer

A)  $y = ( x + 3 ) ^ { 2 }$ 
B)  $y = x ^ { 2 } - 3$ 
C)  $y = ( x - 3 ) ^ { 2 }$ 
D)  $y = x ^ { 2 } + 3$ 
A)  $y = ( x + 3 ) ^ { 2 }$ 
B)  $y = x ^ { 2 } - 3$ 
C)  $y = ( x - 3 ) ^ { 2 }$ 
D)  $y = x ^ { 2 } + 3$

Question 14

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $\{ 5,8,13 \}$; range: $\{ 4,7,12 \}$ 
B)  domain: $\{ 4,7,12 \}$; range: $\{ 5,8,13 \}$ 
C)  domain: $\{ 4,12 \}$; range: $\{ 5,13 \}$ 
D)  None of these 
A)  domain: $\{ 5,8,13 \}$; range: $\{ 4,7,12 \}$ 
B)  domain: $\{ 4,7,12 \}$; range: $\{ 5,8,13 \}$ 
C)  domain: $\{ 4,12 \}$; range: $\{ 5,13 \}$ 
D)  None of these

Question 15

Graph the line and give the domain and the range.
-$y-2=0$

Accepted Answer

A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 2 \}$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = \{ 2 \} , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 2 \}$
  
A)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 2 \}$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = \{ 2 \} , \mathrm { R } = ( - \infty , \infty )$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 2 \}$

Question 16

Decide whether the relation defines a function.
-$$y = x ^ { 3 }$$

Accepted Answer

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

Question 17

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $( - \infty , 0 ] \cup [ 0 , \infty )$; range: $( - \infty , 4 ] \cup [ 4 , \infty )$ 
B)  domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , 4 ) \cup ( 4 , \infty )$ 
A)  domain: $( - \infty , 0 ] \cup [ 0 , \infty )$; range: $( - \infty , 4 ] \cup [ 4 , \infty )$ 
B)  domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , 4 ) \cup ( 4 , \infty )$

Question 18

Determine whether the three points are collinear.
-(6, -2), (-2, 5), (1, 1)

Accepted Answer

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

Question 19

Use a graphing calculator to solve the linear equation.
-The graph of $y _ { 1 }$ is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation $\mathrm { y } _ { 1 } = 0$ ?

$$- 90 , - \frac { 91 } { 10 } , \frac { 91 } { 10 } , 85$$

Accepted Answer

A)  $\frac { 91 } { 10 }$ 
B)  85 
C)  $- 90$ 
D)  $- \frac { 91 } { 10 }$ 
A)  $\frac { 91 } { 10 }$ 
B)  85 
C)  $- 90$ 
D)  $- \frac { 91 } { 10 }$

Question 20

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x).
-$$h ( x ) = \frac { 9 } { \sqrt { 10 x + 7 } }$$

Accepted Answer

A)  $f ( x ) = \frac { 9 } { \sqrt { x } } , g ( x ) = 10 x + 7$ 
B)  $f ( x ) = \sqrt { 10 x + 7 } , g ( x ) = 9$ 
C)  $f ( x ) = 9 , g ( x ) = \sqrt { 10 + 7 }$ 
D)  $f ( x ) = \frac { 9 } { x } , g ( x ) = 10 x + 7$ 
A)  $f ( x ) = \frac { 9 } { \sqrt { x } } , g ( x ) = 10 x + 7$ 
B)  $f ( x ) = \sqrt { 10 x + 7 } , g ( x ) = 9$ 
C)  $f ( x ) = 9 , g ( x ) = \sqrt { 10 + 7 }$ 
D)  $f ( x ) = \frac { 9 } { x } , g ( x ) = 10 x + 7$

Describe the transformations and give the equation for the graph. -

Graph the function. - $f ( x ) = \frac { 1 } { 2 } \sqrt { - x }$ $Graph the function. - f ( x ) = \frac { 1 } { 2 } \sqrt { - x }$

Solve the problem. -A deep sea diving bell is being lowered at a constant rate. After 11 minutes, the bell is at a depth of 500 ft. After 40 minutes the bell is at a depth of 1800 ft. What is the average rate of change of Depth? Round to one decimal place.

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. -

Find the average rate of change illustrated in the graph. -

Find the requested function value. -Find $( g \circ f ) ( - 9 )$ when $f ( x ) = 4 x + 5$ and $g ( x ) = - 5 x ^ { 2 } + 5 x - 6$

Solve the problem. -The graph shows an idealized linear relationship for the average monthly payment to retirees from 1995 to 1999. Use the midpoint formula to estimate the average payment in 1997. Average Monthly Payment to Retirees

Find the requested function value. -Find $( f \circ g ) ( 9 )$ when $f ( x ) = 8 x - 5$ and $g ( x ) = 3 x ^ { 2 } - 5 x + 9$ .

Solve the problem. -The table lists how financial aid income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the financial aid cutoff for 1985.

Give the domain and range of the relation. - $x y = - 2$

Solve the problem. -

Evaluate. -Find (f + g)(-3) when f(x) = x - 5 and g(x) = x + 3.

Solve the problem. -Select the equation that describes the graph shown.

Give the domain and range of the relation. -

Graph the line and give the domain and the range. - $y-2=0$

Decide whether the relation defines a function. - $y = x ^ { 3 }$

Give the domain and range of the relation. -

Determine whether the three points are collinear. -(6, -2), (-2, 5), (1, 1)

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 9 } { \sqrt { 10 x + 7 } }$

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

Describe the transformations and give the equation for the graph. -

Graph the function. - f(x)=12−xf ( x ) = \frac { 1 } { 2 } \sqrt { - x }f(x)=21​−x​

Solve the problem. -A deep sea diving bell is being lowered at a constant rate. After 11 minutes, the bell is at a depth of 500 ft. After 40 minutes the bell is at a depth of 1800 ft. What is the average rate of change of Depth? Round to one decimal place.

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. -

Find the average rate of change illustrated in the graph. -

Find the requested function value. -Find (g∘f)(−9)( g \circ f ) ( - 9 )(g∘f)(−9) when f(x)=4x+5f ( x ) = 4 x + 5f(x)=4x+5 and g(x)=−5x2+5x−6g ( x ) = - 5 x ^ { 2 } + 5 x - 6g(x)=−5x2+5x−6

Solve the problem. -The graph shows an idealized linear relationship for the average monthly payment to retirees from 1995 to 1999. Use the midpoint formula to estimate the average payment in 1997. Average Monthly Payment to Retirees

Find the requested function value. -Find (f∘g)(9)( f \circ g ) ( 9 )(f∘g)(9) when f(x)=8x−5f ( x ) = 8 x - 5f(x)=8x−5 and g(x)=3x2−5x+9g ( x ) = 3 x ^ { 2 } - 5 x + 9g(x)=3x2−5x+9 .

Solve the problem. -The table lists how financial aid income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the financial aid cutoff for 1985.

Give the domain and range of the relation. - xy=−2x y = - 2xy=−2

Solve the problem. -

Evaluate. -Find (f + g)(-3) when f(x) = x - 5 and g(x) = x + 3.

Solve the problem. -Select the equation that describes the graph shown.

Give the domain and range of the relation. -

Graph the line and give the domain and the range. - y−2=0y-2=0y−2=0

Decide whether the relation defines a function. - y=x3y = x ^ { 3 }y=x3

Give the domain and range of the relation. -

Determine whether the three points are collinear. -(6, -2), (-2, 5), (1, 1)

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - h(x)=910x+7h ( x ) = \frac { 9 } { \sqrt { 10 x + 7 } }h(x)=10x+7​9​

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

Graph the function. - $f ( x ) = \frac { 1 } { 2 } \sqrt { - x }$ $Graph the function. - f ( x ) = \frac { 1 } { 2 } \sqrt { - x }$

Find the requested function value. -Find $( g \circ f ) ( - 9 )$ when $f ( x ) = 4 x + 5$ and $g ( x ) = - 5 x ^ { 2 } + 5 x - 6$

Find the requested function value. -Find $( f \circ g ) ( 9 )$ when $f ( x ) = 8 x - 5$ and $g ( x ) = 3 x ^ { 2 } - 5 x + 9$ .

Give the domain and range of the relation. - $x y = - 2$

Graph the line and give the domain and the range. - $y-2=0$

Decide whether the relation defines a function. - $y = x ^ { 3 }$

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 9 } { \sqrt { 10 x + 7 } }$