Question 1

Write an equation for the line described. Give your answer in slope-intercept form.
-$m = 8$, through $( 2 , - 7 )$

Accepted Answer

A)  $y = 8 x + 22$ 
B)  $y = 8 x - 21$ 
C)  $y = 8 x - 23$ 
D)  $y = 9 x + 24$ 
A)  $y = 8 x + 22$ 
B)  $y = 8 x - 21$ 
C)  $y = 8 x - 23$ 
D)  $y = 9 x + 24$

Question 2

Determine whether the three points are collinear.
-$( 8 , - 4 ) , ( - 5,8 ) , ( 1,1 )$

Accepted Answer

A) True 
 B)False

Question 3

A circle has a diameter with endpoints $( - 2,1 )$ and $( 18,17 )$. Find the coordinates of the center.

Accepted Answer

A)  $( 16,18 )$ 
B)  $( - 12 , - 7 )$ 
C)  $( 8,9 )$ 
D)  $( 38,33 )$ 
A)  $( 16,18 )$ 
B)  $( - 12 , - 7 )$ 
C)  $( 8,9 )$ 
D)  $( 38,33 )$

Question 4

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

Accepted Answer

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

Question 5

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-During which hour did the temperature increase the most?

Accepted Answer

A)  1 p.m. to 2 p.m. 
B)  12 p.m. to 1 p.m. 
C)  9 a.m. to 10 a.m. 
D)  10 a.m. to 11 a.m. 
A)  1 p.m. to 2 p.m. 
B)  12 p.m. to 1 p.m. 
C)  9 a.m. to 10 a.m. 
D)  10 a.m. to 11 a.m.

Question 6

Decide whether the relation defines a function.
-$$\begin{array}{l}
\text { Student Test Score }\
\begin{array} { r | r } 
\text { Name } & \text { Test Score } \
\hline \text { Bob L. } & 85 \
\hline \text { Susan H. } & 83 \
\hline \text { Jim H. } & 85 \
\hline \text { Bruce B. } & 96
\end{array}
\end{array}$$

Accepted Answer

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

Question 7

Describe how the graph of the equation relates to the graph $$y = x ^ { 2 }$$
-$$f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 6$$

Accepted Answer

A)  vertical stretching by a factor of 5 and a translation 6 units to the right 
B)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 6 units down 
C)  vertical stretching by a factor of 5 and a translation 6 units down 
D)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 6 units to the left 
A)  vertical stretching by a factor of 5 and a translation 6 units to the right 
B)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 6 units down 
C)  vertical stretching by a factor of 5 and a translation 6 units down 
D)  vertical shrinking by a factor of $\frac { 1 } { 5 }$ and a translation 6 units to the left

Question 8

Find the slope and the y-intercept of the line.
-$$y - \frac { 8 } { 5 } x + 3 = 0$$

Accepted Answer

A)  slope: $\frac { 8 } { 5 } ; y$-intercept $( 0 , - 3 )$ 
B)  slope: $- 3 ; y$-intercept: $\left( 0 , \frac { 8 } { 5 } \right)$ 
C)  slope: $3 ; y$-intercept: $\left( 0 , - \frac { 8 } { 5 } \right)$ 
D)  slope: $\frac { 8 } { 5 } ; y$-intercept: $( 0,3 )$ 
A)  slope: $\frac { 8 } { 5 } ; y$-intercept $( 0 , - 3 )$ 
B)  slope: $- 3 ; y$-intercept: $\left( 0 , \frac { 8 } { 5 } \right)$ 
C)  slope: $3 ; y$-intercept: $\left( 0 , - \frac { 8 } { 5 } \right)$ 
D)  slope: $\frac { 8 } { 5 } ; y$-intercept: $( 0,3 )$

Question 9

Find the slope of the line satisfying the given conditions.
-through $( 5,5 )$ and $( - 2,5 )$

Accepted Answer

A)  $- 7$ 
B)  undefined 
C)  7 
D)  0 
A)  $- 7$ 
B)  undefined 
C)  7 
D)  0

Question 10

Give the domain and range of the relation.
-Find $g ( a - 1 )$ when $g ( x ) = \frac { 1 } { 4 } x - 1$

Accepted Answer

A)  $\frac { a - 5 } { 4 }$ 
B)  $\frac { a + 5 } { 4 }$ 
C)  $\frac { 1 } { 4 } a - 4$ 
D)  $\frac { 1 } { 4 } a - 1$ 
A)  $\frac { a - 5 } { 4 }$ 
B)  $\frac { a + 5 } { 4 }$ 
C)  $\frac { 1 } { 4 } a - 4$ 
D)  $\frac { 1 } { 4 } a - 1$

Question 11

For the given functions f and g , find the indicated composition.
-$$f ( x ) = \sqrt { x + 4 } , \quad g ( x ) = - \frac { 5 } { x }$$
$( g f ) ( x )$

Accepted Answer

A)  $- \frac { 1 } { \sqrt { 5 x + 4 } }$ 
B)  $\sqrt { - \frac { 5 } { x } + 4 }$ 
C)  $\frac { 5 } { \sqrt { - x + 4 } }$ 
D)  $- \frac { 5 } { \sqrt { x + 4 } }$ 
A)  $- \frac { 1 } { \sqrt { 5 x + 4 } }$ 
B)  $\sqrt { - \frac { 5 } { x } + 4 }$ 
C)  $\frac { 5 } { \sqrt { - x + 4 } }$ 
D)  $- \frac { 5 } { \sqrt { x + 4 } }$

Question 12

Match the description with the correct symbolic expression.
-a linear equation whose graph has $x$-intercept $- 5$ and $y$-intercept 11

Accepted Answer

A)  $- 11 x + 5 y = 55$ 
B)  $x = 11$ 
C)  $y = 11 x + 55$ 
D)  $f ( x ) = - 5$ 
A)  $- 11 x + 5 y = 55$ 
B)  $x = 11$ 
C)  $y = 11 x + 55$ 
D)  $f ( x ) = - 5$

Question 13

Give a rule for the piecewise-defined function. Then give the domain and range.
-$f(x)=\llbracket x \rrbracket-1$

Accepted Answer

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

Question 14

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } - 2 x + 10 y - 55 = 0$$

Accepted Answer

A)  center: $( - 5,1 )$; radius: 9 
B)  center: $( 5 , - 1 )$; radius: 81 
C)  center: $( - 1,5 )$; radius: 81 
D)  center: $( 1 , - 5 )$; radius: 9 
A)  center: $( - 5,1 )$; radius: 9 
B)  center: $( 5 , - 1 )$; radius: 81 
C)  center: $( - 1,5 )$; radius: 81 
D)  center: $( 1 , - 5 )$; radius: 9

Question 15

Determine the intervals of the domain over which the function is continuous.
-

Accepted Answer

A)  $( - \infty , 1 ) \cup ( 1 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $[ 4 , \infty )$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
A)  $( - \infty , 1 ) \cup ( 1 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $[ 4 , \infty )$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$

Question 16

Give the domain and range of the relation.
-Find $f ( - 3 )$ when $f ( x ) = 3 x - 1$

Accepted Answer

A)  2 
B)  $- 10$ 
C)  $- 6$ 
D)  $- 8$ 
A)  2 
B)  $- 10$ 
C)  $- 6$ 
D)  $- 8$

Question 17

Use the graph to solve the problem.
-$$\text { The surface area a of a cylinder is shown in the graph below. What is the radius } \mathrm { r } \text { if the surface area is } 20 \mathrm {~m} 2 \text { ? }$$

Accepted Answer

A)  1.2 m 
B)  0.6 m 
C)  0.8 m 
D)  1.0 m 
A)  1.2 m 
B)  0.6 m 
C)  0.8 m 
D)  1.0 m

Question 18

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
number for both groups. Use the graph to answer the question.  
-The cost of manufacturing clocks is given by $C ( x ) = 56 + 31 x - x ^ { 2 }$. Also, it is known that in thours the number of clocks that can be produced is given by $x = 12 t$, where $1 \leq t \leq 12$. Express $C$ as a function of $t$.

Accepted Answer

A)  $C ( t ) = 56 + 31 t + t ^ { 2 }$ 
B)  $C ( t ) = 56 + 372 t - 144 t ^ { 2 }$ 
C)  $C ( t ) = 56 + 31 \mathrm { t } - 12$ 
D)  $C ( t ) = 56 + 372 t - 144 t$ 
A)  $C ( t ) = 56 + 31 t + t ^ { 2 }$ 
B)  $C ( t ) = 56 + 372 t - 144 t ^ { 2 }$ 
C)  $C ( t ) = 56 + 31 \mathrm { t } - 12$ 
D)  $C ( t ) = 56 + 372 t - 144 t$

Question 19

Describe the transformations and give the equation for the graph.
-Find $\left( \frac { f } { g } \right) ( - 5 )$ when $f ( x ) = 4 x - 2$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 2$

Accepted Answer

A)  $- \frac { 22 } { 57 }$ 
B)  $\frac { 5 } { 18 }$ 
C)  $\frac { 4 } { 57 }$ 
D)  $\frac { 5 } { 57 }$ 
A)  $- \frac { 22 } { 57 }$ 
B)  $\frac { 5 } { 18 }$ 
C)  $\frac { 4 } { 57 }$ 
D)  $\frac { 5 } { 57 }$

Question 20

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (-8, 7), endpoint (-4, 6)

Accepted Answer

A)  (-2, -2) 
B)  (4, 4) 
C)  (-12, 5) 
D)  (-12, 8) 
A)  (-2, -2) 
B)  (4, 4) 
C)  (-12, 5) 
D)  (-12, 8)

Write an equation for the line described. Give your answer in slope-intercept form. - $m = 8$ , through $( 2 , - 7 )$

Determine whether the three points are collinear. - $( 8 , - 4 ) , ( - 5,8 ) , ( 1,1 )$

A circle has a diameter with endpoints $( - 2,1 )$ and $( 18,17 )$ . Find the coordinates of the center.

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

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -During which hour did the temperature increase the most?

Decide whether the relation defines a function. - Student Test Score Name Test Score Bob L. 85 Susan H. 83 Jim H. 85 Bruce B. 96

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 6$

Find the slope and the y-intercept of the line. - $y - \frac { 8 } { 5 } x + 3 = 0$

Find the slope of the line satisfying the given conditions. -through $( 5,5 )$ and $( - 2,5 )$

Give the domain and range of the relation. -Find $g ( a - 1 )$ when $g ( x ) = \frac { 1 } { 4 } x - 1$

For the given functions f and g , find the indicated composition. - $f ( x ) = \sqrt { x + 4 } , \quad g ( x ) = - \frac { 5 } { x }$ $( g f ) ( x )$

Match the description with the correct symbolic expression. -a linear equation whose graph has $x$ -intercept $- 5$ and $y$ -intercept 11

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x)=\llbracket x \rrbracket-1$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x)=\llbracket x \rrbracket-1$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 2 x + 10 y - 55 = 0$

Determine the intervals of the domain over which the function is continuous. -

Give the domain and range of the relation. -Find $f ( - 3 )$ when $f ( x ) = 3 x - 1$

Describe the transformations and give the equation for the graph. -Find $\left( \frac { f } { g } \right) ( - 5 )$ when $f ( x ) = 4 x - 2$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 2$

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (-8, 7), endpoint (-4, 6)

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

Write an equation for the line described. Give your answer in slope-intercept form. - m=8m = 8m=8 , through (2,−7)( 2 , - 7 )(2,−7)

Determine whether the three points are collinear. - (8,−4),(−5,8),(1,1)( 8 , - 4 ) , ( - 5,8 ) , ( 1,1 )(8,−4),(−5,8),(1,1)

A circle has a diameter with endpoints (−2,1)( - 2,1 )(−2,1) and (18,17)( 18,17 )(18,17) . Find the coordinates of the center.

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