Question 1

Plot the points below whose coordinates are given on a Cartesian coordinate system. $( 0,8 ) , ( - 8,5 ) , ( - 2 , - 2 ) , ( 5,0 )$

Accepted Answer

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

Question 2

The cost of sending an overnight package from New York to Atlanta is $9.80 for up to, but not including, the first pound and $3.50 for each additional pound (or portion of a pound). A model for the total cost $C$ of sending the package is $C = 9.80 + 3.50$$\lfloor x \rfloor,$ $x > 0,$ where $x$ is the weight of the package (in pounds). Sketch the graph of this function. Note that the function $\lfloor x \rfloor$ is the greatest integer function.

Accepted Answer

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

Question 3

Describe the sequence of transformations from $f ( x ) = \sqrt { x }$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $g ( x ) = \sqrt { x - 3 }$

Accepted Answer

A) Shifted 5 units downward   
B) Shifted 1 unit upward   
C) Shifted 4 units to the left   
D) Shifts 3 units to the right   
E) 4 units to the left and 2 units upward   
A) Shifted 5 units downward   
B) Shifted 1 unit upward   
C) Shifted 4 units to the left   
D) Shifts 3 units to the right   
E) 4 units to the left and 2 units upward

Question 4

Find all real values of x such that f (x) = 0. $f ( x ) = \frac { 7 x - 4 } { 5 }$

Accepted Answer

A)  $\frac { 4 } { 35 }$ 
B)  $\pm \frac { 4 } { 35 }$ 
C)  $\pm \frac { 4 } { 7 }$ 
D)  $\frac { 4 } { 7 }$ 
E)  $- \frac { 4 } { 7 }$ 
A)  $\frac { 4 } { 35 }$ 
B)  $\pm \frac { 4 } { 35 }$ 
C)  $\pm \frac { 4 } { 7 }$ 
D)  $\frac { 4 } { 7 }$ 
E)  $- \frac { 4 } { 7 }$

Question 5

The point $( 3,9 )$ on the graph of $f ( x ) = x ^ { 2 }$ has been shifted to the point $( 4,7 )$ after a rigid transformation. Identify the shift and write the new function $g$ in terms of $f$ .

Accepted Answer

A) Shift: shifted 1 unit to the left. $h ( x ) = ( x + 1 ) ^ { 2 }$ 
B) Shift: horizontally 3 units to the left and vertically 2 units downward. $h ( x ) = ( x + 3 ) ^ { 2 } - 2$ 
C) Shift: horizontally 2 units to the right and vertically 1 unit upward. $h ( x ) = ( x - 2 ) ^ { 2 } + 1$ 
D) Shift: horizontally 1 unit to the right and vertically 2 units downward. $h ( x ) = ( x - 1 ) ^ { 2 } - 2$ 
E) Shift: shifted 1 unit upward. $h ( x ) = x ^ { 2 } + 1$ 
A) Shift: shifted 1 unit to the left. $h ( x ) = ( x + 1 ) ^ { 2 }$ 
B) Shift: horizontally 3 units to the left and vertically 2 units downward. $h ( x ) = ( x + 3 ) ^ { 2 } - 2$ 
C) Shift: horizontally 2 units to the right and vertically 1 unit upward. $h ( x ) = ( x - 2 ) ^ { 2 } + 1$ 
D) Shift: horizontally 1 unit to the right and vertically 2 units downward. $h ( x ) = ( x - 1 ) ^ { 2 } - 2$ 
E) Shift: shifted 1 unit upward. $h ( x ) = x ^ { 2 } + 1$

Question 6

Assuming that the graph shown has y-axis symmetry, sketch the complete graph.

Accepted Answer

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

Question 7

Evaluate $\left( \frac { f } { g } \right) ( 8 )$ where $f ( x ) = x ^ { 2 } - 6 x - 135$ and $g ( x ) = 17 x + 14.$

Accepted Answer

A)  $- \frac { 7 } { 6 }$ 
B)  $- \frac { 119 } { 150 }$ 
C)  $- \frac { 119 } { 22 }$ 
D)  $\frac { 8 } { 75 }$ 
E)  $- \frac { 71 } { 150 }$ 
A)  $- \frac { 7 } { 6 }$ 
B)  $- \frac { 119 } { 150 }$ 
C)  $- \frac { 119 } { 22 }$ 
D)  $\frac { 8 } { 75 }$ 
E)  $- \frac { 71 } { 150 }$

Question 8

Assume that y is directly proportional to x. If $x = 36$ and $y = 27$ , determine a linear model that relates y and x.

Accepted Answer

A)  $y = \frac { 4 } { 3 } x$ 
B)  $y = \frac { 3 } { 5 } x$ 
C)  $y = \frac { 3 } { 2 } x$ 
D)  $y = \frac { 3 } { 4 } x$ 
E)  $y = \frac { 2 } { 3 } x$ 
A)  $y = \frac { 4 } { 3 } x$ 
B)  $y = \frac { 3 } { 5 } x$ 
C)  $y = \frac { 3 } { 2 } x$ 
D)  $y = \frac { 3 } { 4 } x$ 
E)  $y = \frac { 2 } { 3 } x$

Question 9

The weekly profit $P$ (in hundreds of dollars) for a business from a product is given by the model $P ( x ) = 70 - 20 x + 0.8 x ^ { 2 },$ $0 \leq x \leq 20$ where $x$ is the amount (in hundreds of dollars) spent on advertising. Rewrite the profit equation so that $x$ measures advertising expenditures in dollars.

Accepted Answer

A)  $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.8 x ^ { 2 }$ 
B)  $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.00008 x ^ { 2 }$ 
C)  $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.008 x ^ { 2 }$ 
D)  $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.00008 x ^ { 2 }$ 
E)  $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.008 x ^ { 2 }$ 
A)  $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.8 x ^ { 2 }$ 
B)  $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.00008 x ^ { 2 }$ 
C)  $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.008 x ^ { 2 }$ 
D)  $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.00008 x ^ { 2 }$ 
E)  $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.008 x ^ { 2 }$

Question 10

Find the domain of the function. $q ( w ) = \sqrt { 1 - w ^ { 2 } }$

Accepted Answer

A) -1 F1F1F1S1?F1F1F10 w F1F1F1S1??F1F1F101 
B) w F1F1F1S1??F1F1F10-1 or w F1F1F1S1?F1F1F10 1 
C) w F1F1F1S1?F1F1F10 0 
D) w F1F1F1S1?F1F1F10 1 
E) all real numbers 
A) -1 F1F1F1S1?F1F1F10 w F1F1F1S1??F1F1F101 
B) w F1F1F1S1??F1F1F10-1 or w F1F1F1S1?F1F1F10 1 
C) w F1F1F1S1?F1F1F10 0 
D) w F1F1F1S1?F1F1F10 1 
E) all real numbers

Question 11

After completing the table, use the resulting solution points to sketch the graph of the equation $y = x ^ { 2 } - 4 x$ . $$\begin{array} { | c | c | c | c | c | c | } 
\hline x & 0 & 1 & 2 & 3 & 4 \
\hline y & & & & & \
\hline ( x , y ) & & & & & \
\hline
\end{array}$$

Accepted Answer

The answer of After completing the table, use the resulting...

Question 12

Graph the following equation by plotting points that satisfy the equation. $y = | x + 1 | - 2$

Accepted Answer

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

Question 13

Find the midpoint of the line segment joining the points. (0, 9), (4, -3)

Accepted Answer

A) (-2, -3) 
B) (3, 2) 
C) (6, -2) 
D) (-2, 6) 
E) (2, 3) 
A) (-2, -3) 
B) (3, 2) 
C) (6, -2) 
D) (-2, 6) 
E) (2, 3)

Question 14

Consider the graph of $f ( x ) = x ^ { 3 }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $f$ is shifted four units to the right.

Accepted Answer

A)  $y = ( x + 4 ) ^ { 3 }$ 
B)  $y = ( x - 4 ) ^ { 3 }$ 
C)  $y = x ^ { 3 } - 4$ 
D)  $y = x ^ { 3 } + 4$ 
E)  $y = - 4 x ^ { 3 }$ 
A)  $y = ( x + 4 ) ^ { 3 }$ 
B)  $y = ( x - 4 ) ^ { 3 }$ 
C)  $y = x ^ { 3 } - 4$ 
D)  $y = x ^ { 3 } + 4$ 
E)  $y = - 4 x ^ { 3 }$

Question 15

The population $y$ (in millions of people) of North America from 1980 to 2050 can be modeled by $y = 5.3 x + 430,$ $- 30 \leq x \leq 40$ where $x$ represents the year, with $x = 40$ corresponding to 2050. Find the y-intercept of the graph of the model. What does it represent in the given situation?

Accepted Answer

A)  $( 0,483 );$ It represents the population (in millions of people)of North America in 2020. 
B)  $( 0,536 );$ It represents the population (in millions of people)of North America in 2030. 
C)  $( 0,377 );$ It represents the population (in millions of people)of North America in 2000. 
D)  $( 0,430 );$ It represents the population (in millions of people)of North America in 2010. 
E)  $( 0,324 );$ It represents the population (in millions of people)of North America in 1990. 
A)  $( 0,483 );$ It represents the population (in millions of people)of North America in 2020. 
B)  $( 0,536 );$ It represents the population (in millions of people)of North America in 2030. 
C)  $( 0,377 );$ It represents the population (in millions of people)of North America in 2000. 
D)  $( 0,430 );$ It represents the population (in millions of people)of North America in 2010. 
E)  $( 0,324 );$ It represents the population (in millions of people)of North America in 1990.

Question 16

Identify the transformation shown in the graph and identify the associated common function. Write the equation of the graphed function.

Accepted Answer

A) Common function: $y = x ^ { 3 }$ Transformation: horizontal shift 2 units to the rightEquation: $y = ( x - 2 ) ^ { 3 }$ 
B) Common function: $y = x$ Transformation: multiplied by $\frac { 1 } { 2 }$ shrinkingEquation: $y = \frac { 1 } { 2 } x$ 
C) Common function: $y = x ^ { 2 }$ Transformation: reflection about the x-axisEquation: $y = - x ^ { 2 }$ 
D) Common function: $y = c$ Transformation: $c$ is 7.Equation: $y = 7$ 
E) Common function: $y = \sqrt { x }$ Transformation: reflection about the x-axis and a vertical shift 1 unit upwardEquation: $y = - \sqrt { x } + 1$ 
A) Common function: $y = x ^ { 3 }$ Transformation: horizontal shift 2 units to the rightEquation: $y = ( x - 2 ) ^ { 3 }$ 
B) Common function: $y = x$ Transformation: multiplied by $\frac { 1 } { 2 }$ shrinkingEquation: $y = \frac { 1 } { 2 } x$ 
C) Common function: $y = x ^ { 2 }$ Transformation: reflection about the x-axisEquation: $y = - x ^ { 2 }$ 
D) Common function: $y = c$ Transformation: $c$ is 7.Equation: $y = 7$ 
E) Common function: $y = \sqrt { x }$ Transformation: reflection about the x-axis and a vertical shift 1 unit upwardEquation: $y = - \sqrt { x } + 1$

Plot the points below whose coordinates are given on a Cartesian coordinate system. $( 0,8 ) , ( - 8,5 ) , ( - 2 , - 2 ) , ( 5,0 )$

Describe the sequence of transformations from $f ( x ) = \sqrt { x }$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $g ( x ) = \sqrt { x - 3 }$

Find all real values of x such that f (x) = 0. $f ( x ) = \frac { 7 x - 4 } { 5 }$

The point $( 3,9 )$ on the graph of $f ( x ) = x ^ { 2 }$ has been shifted to the point $( 4,7 )$ after a rigid transformation. Identify the shift and write the new function $g$ in terms of $f$ .

Assuming that the graph shown has y-axis symmetry, sketch the complete graph.

Evaluate $\left( \frac { f } { g } \right) ( 8 )$ where $f ( x ) = x ^ { 2 } - 6 x - 135$ and $g ( x ) = 17 x + 14.$

Assume that y is directly proportional to x. If $x = 36$ and $y = 27$ , determine a linear model that relates y and x.

Find the domain of the function. $q ( w ) = \sqrt { 1 - w ^ { 2 } }$

Graph the following equation by plotting points that satisfy the equation. $y = | x + 1 | - 2$

Find the midpoint of the line segment joining the points. (0, 9), (4, -3)

Consider the graph of $f ( x ) = x ^ { 3 }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $f$ is shifted four units to the right.

The population $y$ (in millions of people) of North America from 1980 to 2050 can be modeled by $y = 5.3 x + 430,$ $- 30 \leq x \leq 40$ where $x$ represents the year, with $x = 40$ corresponding to 2050. Find the y-intercept of the graph of the model. What does it represent in the given situation?

Identify the transformation shown in the graph and identify the associated common function. Write the equation of the graphed function.

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

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Exam 3: Functions and Graphs

Plot the points below whose coordinates are given on a Cartesian coordinate system. (0,8),(−8,5),(−2,−2),(5,0)( 0,8 ) , ( - 8,5 ) , ( - 2 , - 2 ) , ( 5,0 )(0,8),(−8,5),(−2,−2),(5,0)

Describe the sequence of transformations from f(x)=xf ( x ) = \sqrt { x }f(x)=x​ to ggg . Then sketch the graph of ggg by hand. Verify with a graphing utility. g(x)=x−3g ( x ) = \sqrt { x - 3 }g(x)=x−3​

Find all real values of x such that f (x) = 0. f(x)=7x−45f ( x ) = \frac { 7 x - 4 } { 5 }f(x)=57x−4​

The point (3,9)( 3,9 )(3,9) on the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 has been shifted to the point (4,7)( 4,7 )(4,7) after a rigid transformation. Identify the shift and write the new function ggg in terms of fff .

Assuming that the graph shown has y-axis symmetry, sketch the complete graph.

Evaluate (fg)(8)\left( \frac { f } { g } \right) ( 8 )(gf​)(8) where f(x)=x2−6x−135f ( x ) = x ^ { 2 } - 6 x - 135f(x)=x2−6x−135 and g(x)=17x+14.g ( x ) = 17 x + 14.g(x)=17x+14.

Assume that y is directly proportional to x. If x=36x = 36x=36 and y=27y = 27y=27 , determine a linear model that relates y and x.

Find the domain of the function. q(w)=1−w2q ( w ) = \sqrt { 1 - w ^ { 2 } }q(w)=1−w2​

After completing the table, use the resulting solution points to sketch the graph of the equation y=x2−4xy = x ^ { 2 } - 4 xy=x2−4x . x 0 1 2 3 4 y (x,y)

Graph the following equation by plotting points that satisfy the equation. y=∣x+1∣−2y = | x + 1 | - 2y=∣x+1∣−2

Find the midpoint of the line segment joining the points. (0, 9), (4, -3)

Consider the graph of f(x)=x3.f ( x ) = x ^ { 3 }.f(x)=x3. Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of fff is shifted four units to the right.

Identify the transformation shown in the graph and identify the associated common function. Write the equation of the graphed function.

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

Plot the points below whose coordinates are given on a Cartesian coordinate system. $( 0,8 ) , ( - 8,5 ) , ( - 2 , - 2 ) , ( 5,0 )$

Describe the sequence of transformations from $f ( x ) = \sqrt { x }$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $g ( x ) = \sqrt { x - 3 }$

Find all real values of x such that f (x) = 0. $f ( x ) = \frac { 7 x - 4 } { 5 }$

The point $( 3,9 )$ on the graph of $f ( x ) = x ^ { 2 }$ has been shifted to the point $( 4,7 )$ after a rigid transformation. Identify the shift and write the new function $g$ in terms of $f$ .

Evaluate $\left( \frac { f } { g } \right) ( 8 )$ where $f ( x ) = x ^ { 2 } - 6 x - 135$ and $g ( x ) = 17 x + 14.$

Assume that y is directly proportional to x. If $x = 36$ and $y = 27$ , determine a linear model that relates y and x.

Find the domain of the function. $q ( w ) = \sqrt { 1 - w ^ { 2 } }$

Graph the following equation by plotting points that satisfy the equation. $y = | x + 1 | - 2$

Consider the graph of $f ( x ) = x ^ { 3 }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $f$ is shifted four units to the right.