Question 1

Give a rule for the piecewise-defined function. Then give the domain and range.
-

Accepted Answer

A) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x \leq - 2 \ 3 & \text { if } x > 1 \end{array} \right.$; Domain: $\{ - 5,3 \}$, Range: $( \infty - 2 ] \cup ( 1 , \infty )$ B) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x 1 \end{array} \right.$; Domain: $( \infty - 2 ] \cup ( 1 , \infty )$, Range: $\{ - 5,3 \}$ D) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x < - 2 \ 3 & \text { if } x \geq 1 \end{array} \right.$; Domain: $\{ - 5,3 \}$, Range: $( \infty - 2 ) \cup [ 1 , \infty )$ A) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x \leq - 2 \ 3 & \text { if } x > 1 \end{array} \right.$; Domain: $\{ - 5,3 \}$, Range: $( \infty - 2 ] \cup ( 1 , \infty )$ B) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x 1 \end{array} \right.$; Domain: $( \infty - 2 ] \cup ( 1 , \infty )$, Range: $\{ - 5,3 \}$ D) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x < - 2 \ 3 & \text { if } x \geq 1 \end{array} \right.$; Domain: $\{ - 5,3 \}$, Range: $( \infty - 2 ) \cup [ 1 , \infty )$

Question 2

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$\mathrm { P } ( 7 , - 8 ) , \mathrm { Q } ( - 7,4 )$$

Accepted Answer

A)  $( 0 , - 4 )$ 
B)  $( 14 , - 12 )$ 
C)  $( 0 , - 2 )$ 
D)  $( 7 , - 6 )$ 
A)  $( 0 , - 4 )$ 
B)  $( 14 , - 12 )$ 
C)  $( 0 , - 2 )$ 
D)  $( 7 , - 6 )$

Question 3

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-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

$$\begin{array} { c c c } 
1995 & 1997 & 1999 \
a = \$ 452 ; b = \$ 524 & &
\end{array}$$

Accepted Answer

A)  $\$ 36$ 
B)  $\$ 488$ 
C)  $\$ 500$ 
D)  $\$ 524$ 
A)  $\$ 36$ 
B)  $\$ 488$ 
C)  $\$ 500$ 
D)  $\$ 524$

Question 4

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x).
-$$h ( x ) = \frac { 10 } { \sqrt { 8 x + 8 } }$$

Accepted Answer

A)  $f ( x ) = \frac { 10 } { x } , g ( x ) = 8 x + 8$ 
B)  $f ( x ) = \sqrt { 8 x + 8 } , g ( x ) = 10$ 
C)  $f ( x ) = 10 , g ( x ) = \sqrt { 8 + 8 }$ 
D)  $f ( x ) = \frac { 10 } { \sqrt { x } } , g ( x ) = 8 x + 8$ 
A)  $f ( x ) = \frac { 10 } { x } , g ( x ) = 8 x + 8$ 
B)  $f ( x ) = \sqrt { 8 x + 8 } , g ( x ) = 10$ 
C)  $f ( x ) = 10 , g ( x ) = \sqrt { 8 + 8 }$ 
D)  $f ( x ) = \frac { 10 } { \sqrt { x } } , g ( x ) = 8 x + 8$

Question 5

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x + 5 , & \text { if } x > 0 \
- 4 , & \text { if } x \leq 0
\end{array} \right.$$

Accepted Answer

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

Question 6

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( 3,8 ) \text {, then plot the point that is symmetric to } ( 3,8 ) \text { with respect to the } x \text {-axis. }$$

Accepted Answer

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

Question 7

Determine if the function is even, odd, or neither.
-$f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 4$

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing $( - \infty , 0 )$; Decreasing $( - \infty , 0 )$ 
C)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , - \infty )$ 
A)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing $( - \infty , 0 )$; Decreasing $( - \infty , 0 )$ 
C)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , - \infty )$

Question 10

Determine whether (f  g)(x) = x and whether (g  f)(x) = x.
-$f ( x ) = \frac { 1 } { x } , g ( x ) = x$

Accepted Answer

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

Question 11

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 12

Provide an appropriate response.
-What is the distance from the point $( \mathrm { c } , \mathrm { w } )$ to the point $( \mathrm { m } , \mathrm { q } )$ ?

Accepted Answer

A)  $\sqrt { ( c - w ) ^ { 2 } + ( m - q ) ^ { 2 } }$ 
B)  $\sqrt { ( m - c ) ^ { 2 } - ( q - w ) ^ { 2 } }$ 
C)  $\sqrt { ( m - c ) ^ { 2 } + ( q - w ) ^ { 2 } }$ 
D)  $[ \sqrt { m - c } + \sqrt { q - w } ] ^ { 2 }$ 
A)  $\sqrt { ( c - w ) ^ { 2 } + ( m - q ) ^ { 2 } }$ 
B)  $\sqrt { ( m - c ) ^ { 2 } - ( q - w ) ^ { 2 } }$ 
C)  $\sqrt { ( m - c ) ^ { 2 } + ( q - w ) ^ { 2 } }$ 
D)  $[ \sqrt { m - c } + \sqrt { q - w } ] ^ { 2 }$

Question 13

Determine whether the three points are the vertices of a right triangle.
-(-7, 4), (-1, 6), (3, -6)

Accepted Answer

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

Question 14

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

Accepted Answer

A)  y = -5 
B)  x = -4 
C)  f(x) = 2x -4 
D)  2x + 9y = -5 
A)  y = -5 
B)  x = -4 
C)  f(x) = 2x -4 
D)  2x + 9y = -5

Question 15

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)  -4 
C)  4 
D)  -1 
A)  1 
B)  -4 
C)  4 
D)  -1

Question 16

Give the domain and range of the relation.
-$$y = \sqrt { 2 x - 6 }$$

Accepted Answer

A)  domain: $[ 3 , \infty )$; range: $[ 0 , \infty )$ 
B)  domain: $[ 3 , \infty )$; range: $( \infty , \infty )$ 
C)  domain: $( \infty , \infty )$; range: $[ 3 , \infty )$ 
D)  domain: $( 3 , \infty ) ;$ range: $[ 0 , \infty )$ 
A)  domain: $[ 3 , \infty )$; range: $[ 0 , \infty )$ 
B)  domain: $[ 3 , \infty )$; range: $( \infty , \infty )$ 
C)  domain: $( \infty , \infty )$; range: $[ 3 , \infty )$ 
D)  domain: $( 3 , \infty ) ;$ range: $[ 0 , \infty )$

Question 17

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
-A furniture store buys 105 footstools from a distributor at a cost of $225 each plus an overhead charge of $40 per order. The retail markup is 30% on the total price paid. Find the profit on the sale
Of one footstool.

Accepted Answer

A)  $67.61 
B)  $67.39 
C)  $67.50 
D)  $6761.00 
A)  $67.61 
B)  $67.39 
C)  $67.50 
D)  $6761.00

Question 18

Write all linear equations in slope-intercept form.
-Suppose that a sales person observes that if an item is priced at $10 per item then 7 items are sold. If x dollars per item. Find the slope-intercept form of the equation of the line.

Accepted Answer

A)  y = -x + 17 
B)  y = -x - 3 
C)  y = x - 3 
D)  y = x + 17 
A)  y = -x + 17 
B)  y = -x - 3 
C)  y = x - 3 
D)  y = x + 17

Question 19

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } - 12 x + 2 y - 44 = 0$$

Accepted Answer

A)  center: $( 6 , - 1 )$; radius: 9 
B)  center: $( 1 , - 6 )$; radius: 81 
C)  center: $( - 6,1 )$; radius: 81 
D)  center: $( - 1,6 )$; radius: 9 
A)  center: $( 6 , - 1 )$; radius: 9 
B)  center: $( 1 , - 6 )$; radius: 81 
C)  center: $( - 6,1 )$; radius: 81 
D)  center: $( - 1,6 )$; radius: 9

Question 20

Write all linear equations in slope-intercept form.
-A house was purchased for $65,000. After 6 years the value of the house was $119,000. Find a linear equation that models the value of the house after x years.

Accepted Answer

A)  y = 9000x 
B)  y = 9000x + 65,000 
C)  y = 119,000 
D)  y = 6x + 65,000 
A)  y = 9000x 
B)  y = 9000x + 65,000 
C)  y = 119,000 
D)  y = 6x + 65,000

Give a rule for the piecewise-defined function. Then give the domain and range. -

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 7 , - 8 ) , \mathrm { Q } ( - 7,4 )$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = \frac { 10 } { \sqrt { 8 x + 8 } }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 , & \text { if } x > 0 \\- 4 , & \text { if } x \leq 0\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } x + 5 , & \text { if } x > 0 \\ - 4 , & \text { if } x \leq 0 \end{array} \right.$

Determine if the function is even, odd, or neither. - $f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 4$

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

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - $f ( x ) = \frac { 1 } { x } , g ( x ) = x$

Decide whether the relation defines a function. -

Provide an appropriate response. -What is the distance from the point $( \mathrm { c } , \mathrm { w } )$ to the point $( \mathrm { m } , \mathrm { q } )$ ?

Determine whether the three points are the vertices of a right triangle. -(-7, 4), (-1, 6), (3, -6)

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

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. -

Give the domain and range of the relation. - $y = \sqrt { 2 x - 6 }$

Write all linear equations in slope-intercept form. -Suppose that a sales person observes that if an item is priced at $10 per item then 7 items are sold. If x dollars per item. Find the slope-intercept form of the equation of the line.

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 12 x + 2 y - 44 = 0$

Write all linear equations in slope-intercept form. -A house was purchased for $65,000. After 6 years the value of the house was $119,000. Find a linear equation that models the value of the house after x years.

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

Give a rule for the piecewise-defined function. Then give the domain and range. -

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(7,−8),Q(−7,4)\mathrm { P } ( 7 , - 8 ) , \mathrm { Q } ( - 7,4 )P(7,−8),Q(−7,4)

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - h(x)=108x+8h ( x ) = \frac { 10 } { \sqrt { 8 x + 8 } }h(x)=8x+8​10​

Graph the function. - f(x)={x+5, if x>0−4, if x≤0f ( x ) = \left\{ \begin{array} { l l } x + 5 , & \text { if } x > 0 \\- 4 , & \text { if } x \leq 0\end{array} \right.f(x)={x+5,−4,​ if x>0 if x≤0​

Determine if the function is even, odd, or neither. - f(x)=x4−2x2−4f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 4f(x)=x4−2x2−4

Graph the function. - h(x)=−x+1+2h ( x ) = \sqrt { - x + 1 } + 2h(x)=−x+1​+2

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - f(x)=1x,g(x)=xf ( x ) = \frac { 1 } { x } , g ( x ) = xf(x)=x1​,g(x)=x

Decide whether the relation defines a function. -

Provide an appropriate response. -What is the distance from the point (c,w)( \mathrm { c } , \mathrm { w } )(c,w) to the point (m,q)( \mathrm { m } , \mathrm { q } )(m,q) ?

Determine whether the three points are the vertices of a right triangle. -(-7, 4), (-1, 6), (3, -6)

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

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. -

Give the domain and range of the relation. - y=2x−6y = \sqrt { 2 x - 6 }y=2x−6​

Write all linear equations in slope-intercept form. -Suppose that a sales person observes that if an item is priced at $10 per item then 7 items are sold. If x dollars per item. Find the slope-intercept form of the equation of the line.

Find the center and radius of the circle. - x2+y2−12x+2y−44=0x ^ { 2 } + y ^ { 2 } - 12 x + 2 y - 44 = 0x2+y2−12x+2y−44=0

Write all linear equations in slope-intercept form. -A house was purchased for $65,000. After 6 years the value of the house was $119,000. Find a linear equation that models the value of the house after x years.

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

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 7 , - 8 ) , \mathrm { Q } ( - 7,4 )$

Consider the function h as defined. Find functions f and g so that (f  g)(x) = h(x). - $h ( x ) = \frac { 10 } { \sqrt { 8 x + 8 } }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 , & \text { if } x > 0 \\- 4 , & \text { if } x \leq 0\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } x + 5 , & \text { if } x > 0 \\ - 4 , & \text { if } x \leq 0 \end{array} \right.$

Determine if the function is even, odd, or neither. - $f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 4$

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

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - $f ( x ) = \frac { 1 } { x } , g ( x ) = x$

Provide an appropriate response. -What is the distance from the point $( \mathrm { c } , \mathrm { w } )$ to the point $( \mathrm { m } , \mathrm { q } )$ ?

Give the domain and range of the relation. - $y = \sqrt { 2 x - 6 }$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 12 x + 2 y - 44 = 0$