Question 1

Graph the function.
-$f(x)=\llbracket x-1 \rrbracket$

Accepted Answer

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

Question 2

Graph the function.
-$$y = \sqrt { x + 5 }$$

Accepted Answer

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

Question 3

Find the slope and the y-intercept of the line.
-$$6 x - 8 y = - 8$$

Accepted Answer

A)  slope: $- \frac { 3 } { 4 } ; y$-intercept: $( 0 , - 1 )$ 
B)  slope: $- \frac { 4 } { 3 } ; y$-intercept: $( 0,1 )$ 
C)  slope: $\frac { 3 } { 4 } ; y$-intercept: $( 0,1 )$ 
D)  slope: $\frac { 4 } { 3 } ; y$-intercept: $( 0 , - 1 )$ 
A)  slope: $- \frac { 3 } { 4 } ; y$-intercept: $( 0 , - 1 )$ 
B)  slope: $- \frac { 4 } { 3 } ; y$-intercept: $( 0,1 )$ 
C)  slope: $\frac { 3 } { 4 } ; y$-intercept: $( 0,1 )$ 
D)  slope: $\frac { 4 } { 3 } ; y$-intercept: $( 0 , - 1 )$

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)  - 2 
B)  $- \frac { 1 } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$ 
A)  - 2 
B)  $- \frac { 1 } { 2 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$

Question 5

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \sqrt { x - 1 } , \quad g ( x ) = - \frac { 7 } { x } \
( g f ) ( x )
\end{array}$$

Accepted Answer

A)  $\sqrt { - \frac { 7 } { x } - 1 }$ 
B)  $- \frac { 1 } { \sqrt { 7 x - 1 } }$ 
C)  $\frac { 7 } { \sqrt { - x - 1 } }$ 
D)  $- \frac { 7 } { \sqrt { x - 1 } }$ 
A)  $\sqrt { - \frac { 7 } { x } - 1 }$ 
B)  $- \frac { 1 } { \sqrt { 7 x - 1 } }$ 
C)  $\frac { 7 } { \sqrt { - x - 1 } }$ 
D)  $- \frac { 7 } { \sqrt { x - 1 } }$

Question 6

Find the slope of the line and sketch the graph.
-$$y + 5 = 0$$

Accepted Answer

A)  m: undefined
  
B)  $m = 0$
  
C)  $m = - \frac { 1 } { 5 }$
  
D)  $\mathrm { m } = - 5$
  
A)  m: undefined
  
B)  $m = 0$
  
C)  $m = - \frac { 1 } { 5 }$
  
D)  $\mathrm { m } = - 5$

Question 7

Write all linear equations in slope-intercept form.
-A company can make 10 bridge bulkheads for $70,800, while 19 bridge bulkheads cost $75,300. Find a linear equation that models the cost to produce x bridge bulkheads.

Accepted Answer

A)  y = 9x + 4500 
B)  y = 500x - 65,800 
C)  y = 500x + 65,800 
D)  y = x + 4500 
A)  y = 9x + 4500 
B)  y = 500x - 65,800 
C)  y = 500x + 65,800 
D)  y = x + 4500

Question 8

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 9

Find the specified domain.
-Find the domain of $( f g ) ( x )$ when $f ( x ) = \frac { 2 } { x - 12 }$ and $g ( x ) = - 4 x - 5$

Accepted Answer

A)  $( - \infty , 12 ) \cup ( 12 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
D)  $( - \infty , - 12 ) \cup ( - 12 , \infty )$ 
A)  $( - \infty , 12 ) \cup ( 12 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
D)  $( - \infty , - 12 ) \cup ( - 12 , \infty )$

Question 10

A new chocolate company is estimating how many candy bars per week college students will consume of their line of
products. The graph shows the probable number of candy bars students (age 18-22) will consume from year 0 to year 10.
B(x) gives the number of candy bars for boys, G(x) gives the number of candy bars for girls, and T(x) gives the total
-The cost of manufacturing clocks is given by $C ( x ) = 60 + 48 x - x ^ { 2 }$. Also, it is known that in $t$ hours the number of clocks that can be produced is given by $x = 6 t$, where $1 \leq t \leq 12$. Express $C$ as a function of $\mathrm { t }$.

Accepted Answer

A)  $C ( t ) = 60 + 48 t + t ^ { 2 }$ 
B)  $C ( t ) = 60 + 288 t - 36 t$ 
C)  $C ( t ) = 60 + 288 t - 36 t ^ { 2 }$ 
D)  $C ( t ) = 60 + 48 t - 6$ 
A)  $C ( t ) = 60 + 48 t + t ^ { 2 }$ 
B)  $C ( t ) = 60 + 288 t - 36 t$ 
C)  $C ( t ) = 60 + 288 t - 36 t ^ { 2 }$ 
D)  $C ( t ) = 60 + 48 t - 6$

Question 11

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-The table shows enrollment in 2-year technical schools for 1980, 1990 and 2000. Assuming a linear relationship, estimate the enrollment for 1995.
 $\begin{array}{c|c}
\text { Year } & \text { Enrollment (in millions) } \
\hline 1980 & 2.2 \
1990 & 2.7 \
2000 & 3.2
\end{array}$

Accepted Answer

A)  $1.25$ million 
B)  $4.65$ million 
C)  $2.2$ million 
D)  $2.95$ million 
A)  $1.25$ million 
B)  $4.65$ million 
C)  $2.2$ million 
D)  $2.95$ million

Question 12

Find the slope of the line and sketch the graph.
-$$3 x + 4 y = 14$$

Accepted Answer

A)  $m = - \frac { 3 } { 4 }$
  
B)  $m = - \frac { 4 } { 3 }$
  
C)  $\mathrm { m } = \frac { 3 } { 4 }$
  
D)  $m = \frac { 4 } { 3 }$
  
A)  $m = - \frac { 3 } { 4 }$
  
B)  $m = - \frac { 4 } { 3 }$
  
C)  $\mathrm { m } = \frac { 3 } { 4 }$
  
D)  $m = \frac { 4 } { 3 }$

Question 13

Find the requested value.
-$f ( - 6 )$ for $f ( x ) = \left\{ \begin{array} { l l } 7 x , & \text { if } x \leq - 1 \ x - 9 , & \text { if } x > - 1 \end{array} \right.$

Accepted Answer

A)  $- 3$ 
B)  $- 42$ 
C)  42 
D)  $- 15$ 
A)  $- 3$ 
B)  $- 42$ 
C)  42 
D)  $- 15$

Question 14

For the points P and Q, find the distance d(P, Q).
-$\mathrm { P } ( - 5 , - 1 ) , \mathrm { Q } ( 7 , - 4 )$

Accepted Answer

A)  $3 \sqrt { 17 }$ 
B)  15 
C)  $135 \sqrt { 15 }$ 
D)  135 
A)  $3 \sqrt { 17 }$ 
B)  15 
C)  $135 \sqrt { 15 }$ 
D)  135

Question 15

Find the specified domain.
-Find the domain of $( f - g ) ( x )$ when $f ( x ) = 6 x - 9$ and $g ( x ) = 6 x - 5$

Accepted Answer

A)  $( - 9,6 )$ 
B)  $( - \infty , \infty )$ 
C)  $( - 6,9 )$ 
D)  $( - 6 , \infty )$ 
A)  $( - 9,6 )$ 
B)  $( - \infty , \infty )$ 
C)  $( - 6,9 )$ 
D)  $( - 6 , \infty )$

Question 16

Find the slope of the line and sketch the graph.
-$2 x-5 y=-6$

Accepted Answer

A)  $m = - \frac { 2 } { 5 }$
  
B)  $m = - \frac { 5 } { 2 }$
  
C)  $m = \frac { 2 } { 5 }$
  
D)  $m = \frac { 5 } { 2 }$
  
A)  $m = - \frac { 2 } { 5 }$
  
B)  $m = - \frac { 5 } { 2 }$
  
C)  $m = \frac { 2 } { 5 }$
  
D)  $m = \frac { 5 } { 2 }$

Question 17

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

Accepted Answer

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

Question 18

Find the center-radius form of the circle described or graphed.
-Find the equation of a circle with center at $( - 4,4 )$, passing through the point $( - 1,8 )$. Write it in center-radius form.

Accepted Answer

A)  $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 5$ 
B)  $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
C)  $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 25$ 
D)  $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ 
A)  $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 5$ 
B)  $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
C)  $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 25$ 
D)  $( x + 4 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$

Question 19

Give the domain and range of the relation.
-

Accepted Answer

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

Question 20

Find the average rate of change illustrated in the graph.
-A deep sea diving bell is being lowered at a constant rate. After 8 minutes, the bell is at a depth of 400 ft. After 45 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)  40.0 ft per minute 
B)  31.1 ft per minute 
C)  37.8 ft per minute 
D)  0.03 ft per minute 
A)  40.0 ft per minute 
B)  31.1 ft per minute 
C)  37.8 ft per minute 
D)  0.03 ft per minute

Graph the function. - $f(x)=\llbracket x-1 \rrbracket$ $Graph the function. - f(x)=\llbracket x-1 \rrbracket$

Graph the function. - $y = \sqrt { x + 5 }$ $Graph the function. - y = \sqrt { x + 5 }$

Find the slope and the y-intercept of the line. - $6 x - 8 y = - 8$

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. -

For the given functions f and g , find the indicated composition. - f(x)=,g(x)=- (gf)(x)

Find the slope of the line and sketch the graph. - $y + 5 = 0$

Write all linear equations in slope-intercept form. -A company can make 10 bridge bulkheads for $70,800, while 19 bridge bulkheads cost $75,300. Find a linear equation that models the cost to produce x bridge bulkheads.

Decide whether the relation defines a function. -

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \frac { 2 } { x - 12 }$ and $g ( x ) = - 4 x - 5$

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -The table shows enrollment in 2-year technical schools for 1980, 1990 and 2000. Assuming a linear relationship, estimate the enrollment for 1995. Year Enrollment (in millions) 1980 2.2 1990 2.7 2000 3.2

Find the slope of the line and sketch the graph. - $3 x + 4 y = 14$

Find the requested value. - $f ( - 6 )$ for $f ( x ) = \left\{ \begin{array} { l l } 7 x , & \text { if } x \leq - 1 \\ x - 9 , & \text { if } x > - 1 \end{array} \right.$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( - 5 , - 1 ) , \mathrm { Q } ( 7 , - 4 )$

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = 6 x - 9$ and $g ( x ) = 6 x - 5$

Find the slope of the line and sketch the graph. - $2 x-5 y=-6$

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

Find the center-radius form of the circle described or graphed. -Find the equation of a circle with center at $( - 4,4 )$ , passing through the point $( - 1,8 )$ . Write it in center-radius form.

Give the domain and range of the relation. -

Find the average rate of change illustrated in the graph. -A deep sea diving bell is being lowered at a constant rate. After 8 minutes, the bell is at a depth of 400 ft. After 45 minutes the bell is at a depth of 1800 ft. What is the average rate of change of depth? Round to one decimal place.

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Graph the function. - f(x)=⟦x−1⟧f(x)=\llbracket x-1 \rrbracketf(x)=[[x−1]]

Graph the function. - y=x+5y = \sqrt { x + 5 }y=x+5​

Find the slope and the y-intercept of the line. - 6x−8y=−86 x - 8 y = - 86x−8y=−8