Question 1

Evaluate $( f + g ) ( 6 )$ where $f ( x ) = x ^ { 2 } - 7 x + 12$ and $g ( x ) = x - 5.$

Accepted Answer

A) -23 
B) 5 
C) 6 
D) 1 
E) 7 
A) -23 
B) 5 
C) 6 
D) 1 
E) 7 E

Question 2

Plot the points and find the slope of the line passing through the pair of points. (1, 0), (-2, 0)

Accepted Answer

A) slope: 0 
B) slope: 1 
C) slope: -3 
D) slope: $- \frac { 1 } { 3 }$ 
E) slope: undefined 
A) slope: 0 
B) slope: 1 
C) slope: -3 
D) slope: $- \frac { 1 } { 3 }$ 
E) slope: undefined A

Question 3

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graphs is shown below.

Accepted Answer

A)  $g ( x ) = ( x - 4 ) ^ { 2 }$ 
B)  $g ( x ) = - ( x + 4 ) ^ { 2 }$ 
C)  $g ( x ) = ( x + 2 ) ^ { 2 }$ 
D)  $g ( x ) = - ( x - 2 ) ^ { 2 }$ 
E)  $g ( x ) = - ( x - 4 ) ^ { 2 }$ 
A)  $g ( x ) = ( x - 4 ) ^ { 2 }$ 
B)  $g ( x ) = - ( x + 4 ) ^ { 2 }$ 
C)  $g ( x ) = ( x + 2 ) ^ { 2 }$ 
D)  $g ( x ) = - ( x - 2 ) ^ { 2 }$ 
E)  $g ( x ) = - ( x - 4 ) ^ { 2 }$ C

Question 4

Which of the following graphs below can be approximated by a linear model? I   II   III

Accepted Answer

A) None can be modeled linearly. 
B) Only graph III can be modeled linearly. 
C) Only graphs I and II can be modeled linearly. 
D) Only graphs I and III can be modeled linearly. 
E) Graphs I, II, and III can be modeled linearly. 
A) None can be modeled linearly. 
B) Only graph III can be modeled linearly. 
C) Only graphs I and II can be modeled linearly. 
D) Only graphs I and III can be modeled linearly. 
E) Graphs I, II, and III can be modeled linearly.

Question 5

The sales tax on an item with a retail price of $612 is $61.20. Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $70.38.

Accepted Answer

A)  $\$ 716.03$ 
B)  $\$ 705.79$ 
C)  $\$ 648.11$ 
D)  $\$ 675.43$ 
E)  $\$ 703.80$ 
A)  $\$ 716.03$ 
B)  $\$ 705.79$ 
C)  $\$ 648.11$ 
D)  $\$ 675.43$ 
E)  $\$ 703.80$

Question 6

Find the x- and y-intercepts of the graph of the equation below. $y = x \sqrt { x + 3 }$

Accepted Answer

A)  $( 3,0 ) , ( 0,3 )$ 
B)  $( 0,0 ) , ( - 3,0 )$ 
C)  $( 0,0 ) , ( 3,0 )$ 
D)  $( 0,0 ) , ( - 3,0 ) , ( 3,0 )$ 
E)  $( 0,0 ) , ( 3,0 ) , ( 0,3 )$ 
A)  $( 3,0 ) , ( 0,3 )$ 
B)  $( 0,0 ) , ( - 3,0 )$ 
C)  $( 0,0 ) , ( 3,0 )$ 
D)  $( 0,0 ) , ( - 3,0 ) , ( 3,0 )$ 
E)  $( 0,0 ) , ( 3,0 ) , ( 0,3 )$

Question 7

You own two fast-food restaurants. During the years 2000 to 2008, the sales for the first restaurant have been increasing according to the function $R _ { 1 } = 323 + 11.8 t,$ $t = 0,1,2,3,4,5,6,7,8$ where $R _ { 1 }$ represents the sales (in thousands of dollars) and $t$ represents the year, with $t = 0$ corresponding to 2000. During the same nine-year period, the sales for the second restaurant have been decreasing according to the function $R _ { 2 } = 470 - 18.6 t,$ $t = 0,1,2,3,4,5,6,7,8.$ Write a function that represents the total sales for the two restaurants to determine whether the total sales have been increasing or decreasing.

Accepted Answer

A)  $R _ { T } = - 147 - 6.8 t,$ total sales have been decreasing. 
B)  $R _ { T } = 793 + 68 t,$ total sales have been increasing. 
C)  $R _ { T } = 793 - 6.8 t,$ total sales have been decreasing. 
D)  $R _ { T } = - 147 + 30.4 t,$ total sales have been increasing. 
E)  $R _ { T } = 147 - 30.4 t,$ total sales have been decreasing. 
A)  $R _ { T } = - 147 - 6.8 t,$ total sales have been decreasing. 
B)  $R _ { T } = 793 + 68 t,$ total sales have been increasing. 
C)  $R _ { T } = 793 - 6.8 t,$ total sales have been decreasing. 
D)  $R _ { T } = - 147 + 30.4 t,$ total sales have been increasing. 
E)  $R _ { T } = 147 - 30.4 t,$ total sales have been decreasing.

Question 8

The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building. Compute the linear regression equation for these data. $\begin{array} { c c } 
\text { Velocity } ( \mathrm { ft } / \mathrm { sec } ) & \text { Distance } ( \mathrm { ft } ) \
15 & 48 \
25 & 80 \
29 & 100 \
33 & 95 \
38 & 112 \
40 & 130 \
48 & 150
\end{array}$

Accepted Answer

A)  $y = 3.02463355 x + 3.626221498$ 
B)  $y = 3.156886228 x + .5988023952$ 
C)  $y = 3.073502956 x + 2.338987407$ 
D)  $y = 3.028222013 x - 1.079962371$ 
E)  $y = 2.944432432 x - 0.7139459459$ 
A)  $y = 3.02463355 x + 3.626221498$ 
B)  $y = 3.156886228 x + .5988023952$ 
C)  $y = 3.073502956 x + 2.338987407$ 
D)  $y = 3.028222013 x - 1.079962371$ 
E)  $y = 2.944432432 x - 0.7139459459$

Question 9

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 10 t + 150.$ The number of hours t needed to produce x products is given by $t ( x ) = 9 x.$ Find the equation representing the cost C of manufacturing x products.

Accepted Answer

A)  $C ( x ) = 90 x + 150$ 
B)  $C ( x ) = 90 x + 1500$ 
C)  $C ( x ) = 19 x + 150$ 
D)  $C ( x ) = 19 x + 160$ 
E)  $C ( x ) = 10 x + 159$ 
A)  $C ( x ) = 90 x + 150$ 
B)  $C ( x ) = 90 x + 1500$ 
C)  $C ( x ) = 19 x + 150$ 
D)  $C ( x ) = 19 x + 160$ 
E)  $C ( x ) = 10 x + 159$

Question 10

Given $q ( x ) = 6 x ^ { 2 } - 3,$ find $q ( 3 ).$

Accepted Answer

A) 33 
B) 15 
C) 51 
D) 54 
E) 57 
A) 33 
B) 15 
C) 51 
D) 54 
E) 57

Question 11

Find (f + g)(x). f (x) = -6x2 + 5x - 2
G(x) = -3x2 + 1

Accepted Answer

A) ( f + g)(x)= -3x4 + 5x - 3 
B) ( f + g)(x)= -9x4 + 5x - 1 
C) ( f + g)(x)= -3x2 + 5x - 3 
D) ( f + g)(x)= -9x2 + 5x - 1 
E) ( f + g)(x)= 9x2 - 5x + 1 
A) ( f + g)(x)= -3x4 + 5x - 3 
B) ( f + g)(x)= -9x4 + 5x - 1 
C) ( f + g)(x)= -3x2 + 5x - 3 
D) ( f + g)(x)= -9x2 + 5x - 1 
E) ( f + g)(x)= 9x2 - 5x + 1

Question 12

Sketch the graph of the equation below. $x ^ { 2 } + y ^ { 2 } = 9$

Accepted Answer

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

Question 13

Given $m ( x ) = 3 x ^ { 2 } - 6,$ find $m ( r ).$

Accepted Answer

A)  $3 r ^ { 2 } - 6$ 
B)  $9 r ^ { 2 } + 36$ 
C)  $- 3 r ^ { 2 }$ 
D)  $9 r ^ { 2 } - 6$ 
E)  $3 r ^ { 2 } - 6 r$ 
A)  $3 r ^ { 2 } - 6$ 
B)  $9 r ^ { 2 } + 36$ 
C)  $- 3 r ^ { 2 }$ 
D)  $9 r ^ { 2 } - 6$ 
E)  $3 r ^ { 2 } - 6 r$

Question 14

Find the x- and y-intercepts of the graph of the following equation. $9 x + 6 y = 11$

Accepted Answer

A) x-int: $\left( \frac { 3 } { 2 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 2 } { 3 } \right)$ 
B) x-int: $\left( \frac { 3 } { 2 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 11 } { 6 } \right)$ 
C) x-int: $\left( \frac { 11 } { 9 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 11 } { 6 } \right)$ 
D) x-int: $\left( \frac { 9 } { 11 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 3 } { 2 } \right)$ 
E) x-int: $\left( \frac { 11 } { 9 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 2 } { 3 } \right)$ 
A) x-int: $\left( \frac { 3 } { 2 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 2 } { 3 } \right)$ 
B) x-int: $\left( \frac { 3 } { 2 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 11 } { 6 } \right)$ 
C) x-int: $\left( \frac { 11 } { 9 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 11 } { 6 } \right)$ 
D) x-int: $\left( \frac { 9 } { 11 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 3 } { 2 } \right)$ 
E) x-int: $\left( \frac { 11 } { 9 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 2 } { 3 } \right)$

Question 15

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Accepted Answer

A)  $f ( x ) = | - 3 x - 1 | + 2$ 
B)  $f ( x ) = | - 3 x + 1 | + 2$ 
C)  $f ( x ) = - 3 | x + 1 | - 2$ 
D)  $f ( x ) = - 3 | x - 1 | + 2$ 
E)  $f ( x ) = - 3 | x + 1 | + 2$ 
A)  $f ( x ) = | - 3 x - 1 | + 2$ 
B)  $f ( x ) = | - 3 x + 1 | + 2$ 
C)  $f ( x ) = - 3 | x + 1 | - 2$ 
D)  $f ( x ) = - 3 | x - 1 | + 2$ 
E)  $f ( x ) = - 3 | x + 1 | + 2$

Question 16

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point$~~~~~~~~~~~~~$Slope
$( - 2,4 )~~~~~~~~$$m = \frac { 1 } { 2 }$ I: $\quad ( 8,6 )$
II: $\quad ( 2,6 )$
III: $\quad ( 4,7 )$

Accepted Answer

A) Only points II and III lie on the line. 
B) Only point II lies on the line. 
C) Only point III lies on the line. 
D) Only points I and II lie on the line. 
E) Only points I and III lie on the line. 
A) Only points II and III lie on the line. 
B) Only point II lies on the line. 
C) Only point III lies on the line. 
D) Only points I and II lie on the line. 
E) Only points I and III lie on the line.

Question 17

The national defense budget expenses $V$ (in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model $$V = \left\{ \begin{array} { c c } 
- 0.326 t ^ { 2 } + 3.40 t + 28.7 , & 0 \leq t \leq 6 \
0.441 t ^ { 2 } - 6.23 t + 62.6 , & 7 \leq t \leq 15
\end{array} \right.$$ where $t$ represents the year, with $t = 0$ corresponding to 1990. Use the model to find total veteran expenses in 1995.

Accepted Answer

A) $61.816 billion 
B) $37.550 billion 
C) $37.364 billion 
D) $32.894 billion 
E) $44.736 billion 
A) $61.816 billion 
B) $37.550 billion 
C) $37.364 billion 
D) $32.894 billion 
E) $44.736 billion

Question 18

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outermost ripple is given by $r ( t ) = 0.5 t$ where $t$ is time in seconds after the pebble strikes the water. The area of the outermost circle is given by the function $A ( r ) = \pi r ^ { 2 }.$ Find and interpret $( A \circ r ) ( t ).$

Accepted Answer

A)  $( A \circ r ) ( t ) = \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$ 
B)  $( A \circ r ) ( t ) = 0.5 \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$ 
C)  $( A \circ r ) ( t ) = 0.25 \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$ 
D)  $( A \circ r ) ( t ) = 0.25 \pi t ^ { 2 };$ $A \circ r$ represents the area of the circle at time $t.$ 
E)  $( A \circ r ) ( t ) = 0.5 \pi t^ { 2 };$ $A \circ r$ represents the area of the circle at time $t.$ 
A)  $( A \circ r ) ( t ) = \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$ 
B)  $( A \circ r ) ( t ) = 0.5 \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$ 
C)  $( A \circ r ) ( t ) = 0.25 \pi t ^ { 2 };$ $A \circ r$ represents the radius of the circle at time $t.$ 
D)  $( A \circ r ) ( t ) = 0.25 \pi t ^ { 2 };$ $A \circ r$ represents the area of the circle at time $t.$ 
E)  $( A \circ r ) ( t ) = 0.5 \pi t^ { 2 };$ $A \circ r$ represents the area of the circle at time $t.$

Question 19

Suppose the average remaining lifetime for women in a given country is given in the following table. $$\begin{array} { | c | c | } 
\hline \text { Age } & \text { Years } \
\hline 5 & 75.2 \
\hline 30 & 54.3 \
\hline 50 & 37.5 \
\hline 65 & 25.4 \
\hline 75 & 17.0 \
\hline
\end{array}$$ Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years. Round parameters to the nearest hundredth.

Accepted Answer

A)  $A ( x ) = - 14.53 x + 44.37$ 
B)  $A ( x ) = - 0.83 x + 44.37$ 
C)  $A ( x ) = - 14.53 x + 85.47$ 
D)  $A ( x ) = - 14.53 x + 79.27$ 
E)  $A ( x ) = - 0.83 x + 79.27$ 
A)  $A ( x ) = - 14.53 x + 44.37$ 
B)  $A ( x ) = - 0.83 x + 44.37$ 
C)  $A ( x ) = - 14.53 x + 85.47$ 
D)  $A ( x ) = - 14.53 x + 79.27$ 
E)  $A ( x ) = - 0.83 x + 79.27$

Question 20

Use the graph of $$f$$ to sketch the graph of $y = f ( x ) + 2$ .

Accepted Answer

A) Horizontal shift 2 units to the right   
B) Reflection in the x-axis   
C) Vertical shift 2 units upward   
D) Horizontal shift 3 units to the left   
E) Stretching by 2   
A) Horizontal shift 2 units to the right   
B) Reflection in the x-axis   
C) Vertical shift 2 units upward   
D) Horizontal shift 3 units to the left   
E) Stretching by 2

Evaluate $( f + g ) ( 6 )$ where $f ( x ) = x ^ { 2 } - 7 x + 12$ and $g ( x ) = x - 5.$

Plot the points and find the slope of the line passing through the pair of points. (1, 0), (-2, 0)

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graphs is shown below. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graphs is shown below.$

Which of the following graphs below can be approximated by a linear model? I II III

The sales tax on an item with a retail price of $612 is $61.20. Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $70.38.

Find the x- and y-intercepts of the graph of the equation below. $y = x \sqrt { x + 3 }$

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 10 t + 150.$ The number of hours t needed to produce x products is given by $t ( x ) = 9 x.$ Find the equation representing the cost C of manufacturing x products.

Given $q ( x ) = 6 x ^ { 2 } - 3,$ find $q ( 3 ).$

Find (f + g)(x). f (x) = -6x2 + 5x - 2 G(x) = -3x2 + 1

Sketch the graph of the equation below. $x ^ { 2 } + y ^ { 2 } = 9$

Given $m ( x ) = 3 x ^ { 2 } - 6,$ find $m ( r ).$

Find the x- and y-intercepts of the graph of the following equation. $9 x + 6 y = 11$

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point $~~~~~$ Slope $( - 2,4 )$ $m = \frac { 1 } { 2 }$ I: $\quad ( 8,6 )$ II: $\quad ( 2,6 )$ III: $\quad ( 4,7 )$

Use the graph of $f$ to sketch the graph of $y = f ( x ) + 2$ .

Fundamental Concepts of Algebra

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

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Probability Web

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Exam 3: Functions and Graphs

Evaluate (f+g)(6)( f + g ) ( 6 )(f+g)(6) where f(x)=x2−7x+12f ( x ) = x ^ { 2 } - 7 x + 12f(x)=x2−7x+12 and g(x)=x−5.g ( x ) = x - 5.g(x)=x−5.

Plot the points and find the slope of the line passing through the pair of points. (1, 0), (-2, 0)

Use the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to write an equation for the function whose graphs is shown below.

Which of the following graphs below can be approximated by a linear model? I II III

The sales tax on an item with a retail price of $612 is $61.20. Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $70.38.

Find the x- and y-intercepts of the graph of the equation below. y=xx+3y = x \sqrt { x + 3 }y=xx+3​

The monthly cost C of running the machinery in a factory for t hours is given by C(t)=10t+150.C ( t ) = 10 t + 150.C(t)=10t+150. The number of hours t needed to produce x products is given by t(x)=9x.t ( x ) = 9 x.t(x)=9x. Find the equation representing the cost C of manufacturing x products.

Given q(x)=6x2−3,q ( x ) = 6 x ^ { 2 } - 3,q(x)=6x2−3, find q(3).q ( 3 ).q(3).

Find (f + g)(x). f (x) = -6x2 + 5x - 2 G(x) = -3x2 + 1

Sketch the graph of the equation below. x2+y2=9x ^ { 2 } + y ^ { 2 } = 9x2+y2=9

Given m(x)=3x2−6,m ( x ) = 3 x ^ { 2 } - 6,m(x)=3x2−6, find m(r).m ( r ).m(r).

Find the x- and y-intercepts of the graph of the following equation. 9x+6y=119 x + 6 y = 119x+6y=11

Use the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ to write an equation for the function whose graph is shown.

Use the graph of fff to sketch the graph of y=f(x)+2y = f ( x ) + 2y=f(x)+2 .

Fundamental Concepts of Algebra

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Evaluate $( f + g ) ( 6 )$ where $f ( x ) = x ^ { 2 } - 7 x + 12$ and $g ( x ) = x - 5.$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graphs is shown below. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graphs is shown below.$

Find the x- and y-intercepts of the graph of the equation below. $y = x \sqrt { x + 3 }$

The monthly cost C of running the machinery in a factory for t hours is given by $C ( t ) = 10 t + 150.$ The number of hours t needed to produce x products is given by $t ( x ) = 9 x.$ Find the equation representing the cost C of manufacturing x products.

Given $q ( x ) = 6 x ^ { 2 } - 3,$ find $q ( 3 ).$

Sketch the graph of the equation below. $x ^ { 2 } + y ^ { 2 } = 9$

Given $m ( x ) = 3 x ^ { 2 } - 6,$ find $m ( r ).$

Find the x- and y-intercepts of the graph of the following equation. $9 x + 6 y = 11$

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Use the graph of $f$ to sketch the graph of $y = f ( x ) + 2$ .