Question 1

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear.
-$$\begin{array} { c | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline y & 9 & 13 & 19 & 27 & 37
\end{array}$$

Accepted Answer

A)  exactly linear 
B)  approximately linear 
C)  nonlinear 
A)  exactly linear 
B)  approximately linear 
C)  nonlinear

Question 2

Solve the equation for y.
-$$6 x - 9 y = 1$$

Accepted Answer

A)  $y = \frac { 3 } { 2 } x + \frac { 1 } { 6 }$ 
B)  $y = \frac { 2 } { 3 } x - \frac { 1 } { 9 }$ 
C)  $y = 6 x - 1$ 
D)  $y = \frac { 2 } { 3 } x + \frac { 1 } { 9 }$ 
A)  $y = \frac { 3 } { 2 } x + \frac { 1 } { 6 }$ 
B)  $y = \frac { 2 } { 3 } x - \frac { 1 } { 9 }$ 
C)  $y = 6 x - 1$ 
D)  $y = \frac { 2 } { 3 } x + \frac { 1 } { 9 }$

Question 3

Solve the system of equations by elimination, if a solution exists.
-$$\left\{ \begin{array} { l } 
6 x - 3 y = - 5 \
18 x - 9 y = 15
\end{array} \right.$$

Accepted Answer

A)  $x = 30 , y = - 15$ 
B)  $x = 0 , y = 0$ 
C)  $x = - 30 , y = 15$ 
D)  No solution 
A)  $x = 30 , y = - 15$ 
B)  $x = 0 , y = 0$ 
C)  $x = - 30 , y = 15$ 
D)  No solution

Question 4

To find the number of units that gives break-even for the product, solve the equation R $$\mathbf { R } = \mathbf { C }$$ ound your answer to the
nearest whole unit.
-Roberto invested some money at 8%, and then invested $2000 more than twice this amount at 10%. His total annual income from the two investments was $3000. How much did he invest at 10%?

Accepted Answer

A)  $22,000 
B)  $20,000 
C)  $6000 
D)  $2200 
A)  $22,000 
B)  $20,000 
C)  $6000 
D)  $2200

Question 5

Solve the inequality and draw a number line graph of the solution.
-$$\frac { 4 } { 5 } ( x + 5 ) > \frac { 3 } { 5 } ( x + 5 )$$

Accepted Answer

A) $x > 5$ B) $x > - 5$ C) $x < - 5$ D) $x < 5$ A) $x > 5$ B) $x > - 5$ C) $x < - 5$ D) $x < 5$

Question 6

Solve the equation for y.
-The temperature of water in a certain lake on a day in October can be determined by using the model $y = 15.2 - 0.537 x$ where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the water 8 degrees? Round
To the nearest foot.

Accepted Answer

A)  69 ft 
B)  32 ft 
C)  43 ft 
D)  13 ft 
A)  69 ft 
B)  32 ft 
C)  43 ft 
D)  13 ft

Question 7

Solve the equation for y.
-The temperature, t, in degrees Fahrenheit, of water being heated is $$65 + \frac { 1 } { 4 } m$$ where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

Accepted Answer

A)  17 min 
B)  40 min 
C)  20 min 
D)  14 min 
A)  17 min 
B)  40 min 
C)  20 min 
D)  14 min

Question 8

Solve the double inequality.
-$- 38 \leq - 5 z + 2$ or $- 5 z + 2 \leq - 8$

Accepted Answer

A)  $2 < z$ or $z < 8$ 
B)  $2 \leq z$ or $z \leq 8$ 
C)  $- 8 < \mathrm { z }$ or $\mathrm { z } < - 2$ 
D)  $- 8 \leq z$ or $z \leq - 2$ 
A)  $2 < z$ or $z < 8$ 
B)  $2 \leq z$ or $z \leq 8$ 
C)  $- 8 < \mathrm { z }$ or $\mathrm { z } < - 2$ 
D)  $- 8 \leq z$ or $z \leq - 2$

Question 9

Write the best-fit linear model for the data.
-The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). The linear model for this data is $\mathrm { y } = 55.8 + 2.79 \mathrm { x }$, where $\mathrm { x }$ is the cost of advertising (in thousands of dollars) and $y$ is number of products sold (in thousands). Use this model to predict the number of products sold (in thousands) if the cost of advertising is $\$ 8000$.
$$\begin{array} { c | r r r r r r r r } 
\text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$$

Accepted Answer

A)  22,375,800 products sold 
B)  75,120 products sold 
C)  78,120 products sold 
D)  84,820 products sold 
A)  22,375,800 products sold 
B)  75,120 products sold 
C)  78,120 products sold 
D)  84,820 products sold

Question 10

Solve the equation.
-$$\frac { 1 } { 3 } ( 9 x - 15 ) = \frac { 1 } { 2 } ( 10 x - 6 )$$

Accepted Answer

A)  $- 1$ 
B)  $- 15$ 
C)  1 
D)  $\frac { 1 } { 15 }$ 
A)  $- 1$ 
B)  $- 15$ 
C)  1 
D)  $\frac { 1 } { 15 }$

Question 11

Solve the inequality and draw a number line graph of the solution.
-$- 11 x - 12 \leq - 12 x - 16$

Accepted Answer

A)  $ d = - 4$
  
B)  $a  - 11$
  
A)  $ d = - 4$
  
B)  $a  - 11$

Question 12

Solve the inequality graphically. Give the solution in interval notation.
-Use the intersection method to solve $- 11 x - 8 \geq - 12 x - 6$

Accepted Answer

A)  $[ 2 , \infty )$ 
B)  $( \infty , 2 ]$ 
C)  $( - 11 , \infty )$ 
D)  $( x , - 11 )$ 
A)  $[ 2 , \infty )$ 
B)  $( \infty , 2 ]$ 
C)  $( - 11 , \infty )$ 
D)  $( x , - 11 )$

Question 13

Find the zero of f(x).
-$$f ( x ) = 6 x + 12$$

Accepted Answer

A)  $- 12$ 
B)  2 
C)  $- 2$ 
D)  12 
A)  $- 12$ 
B)  2 
C)  $- 2$ 
D)  12

Question 14

To find the number of units that gives break-even for the product, solve the equation R $$\mathbf { R } = \mathbf { C }$$ ound your answer to the
nearest whole unit.
-A manufacturer has total revenue given by the function $\mathrm { R } = 130 \mathrm { x }$ and has total cost given by $\mathrm { C } = 112,000 + 10 \mathrm { x }$, where $x$ is the number of units produced and sold.

Accepted Answer

A)  120 units 
B)  140 units 
C)  800 units 
D)  933 units 
A)  120 units 
B)  140 units 
C)  800 units 
D)  933 units

Question 15

Construct a scatter plot of the data in the table.
-$\begin{array}{r|r|r|r|r|r|r}
x & 20 & 23 & -18 & 3 & -23 & -10 \
\hline y & -89 & -43 & 32 & -48 & 68 & -8
\end{array}$

Accepted Answer

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

Question 16

Write the best-fit linear model for the data.
-The ages and lengths of several animals of the same species are recorded in the following table: $\begin{array}{l|l}
\text { Age (months) } & \text { Length (inches) } \
\hline 12 & 9 \
\hline 15 & 12 \
\hline 17 & 20 \
\hline 21 & 21 \
\hline 26 & 24 \
\hline 28 & 27 \
\hline 32 & 35 \
\hline 38 & 40 \
\hline 41 & 40
\end{array}$

\text { Find and then use a linear model to predict the length of a } 35 - \text { month-old animal. }
\end{array}\]

Accepted Answer

A)  37.50 in. 
B)  36.60 in. 
C)  38.50 in. 
D)  35.60 in. 
A)  37.50 in. 
B)  36.60 in. 
C)  38.50 in. 
D)  35.60 in.

Question 17

To find the number of units that gives break-even for the product, solve the equation R $$\mathbf { R } = \mathbf { C }$$ ound your answer to the
nearest whole unit.
-The demand for a certain product is given by p $$p + 8 q = 297 , \text { and the supply is given by } p - 4 q = 21$$ , where p is the price in dollars and q is the quantity demanded or supplied at price p. Find the price at which the quantity
Demanded equals the quantity supplied.

Accepted Answer

A)  $113 
B)  $116 
C)  $115 
D)  $110 
A)  $113 
B)  $116 
C)  $115 
D)  $110

Question 18

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$-intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$.
-

Accepted Answer

A)  a. 0
b. $x = 4$ 
B)  a. 4
b. $x = 0$ 
C)  a. 5
b. $x = 5$ 
D)  a. 4
b. $x = 4$ 
A)  a. 0
b. $x = 4$ 
B)  a. 4
b. $x = 0$ 
C)  a. 5
b. $x = 5$ 
D)  a. 4
b. $x = 4$

Question 19

Provide an appropriate response.
-A set of data consists of the number of years that applicants for foreign service jobs have studied German and
the grades that they receive in a proficiency test in that language. The following linear model is obtained: $$y = 31.6 + 10.9 x$$ , where x represents number of years of study and y represents grade in test. What does the slope
of the model represent in terms of the grades on the test?

Accepted Answer

The slope indicates that grade

Question 20

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if
necessary.
-$\begin{array}{c|ccccc}
x & 10 & 20 & 30 & 40 & 50 \
\hline y & 3.9 & 4.6 & 5.4 & 6.9 & 8.3
\end{array}$

Accepted Answer

A)  $y = x - 8$ 
B)  $y = 0.11 x + 2.49$ 
C)  $y = 0.5 x - 2$ 
D)  $y = 0.17 x + 2.11$ 
A)  $y = x - 8$ 
B)  $y = 0.11 x + 2.49$ 
C)  $y = 0.5 x - 2$ 
D)  $y = 0.17 x + 2.11$

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear. - x 1 2 3 4 5 y 9 13 19 27 37

Solve the equation for y. - $6 x - 9 y = 1$

Solve the system of equations by elimination, if a solution exists. - $\left\{ \begin{array} { l } 6 x - 3 y = - 5 \\18 x - 9 y = 15\end{array} \right.$

Solve the inequality and draw a number line graph of the solution. - $\frac { 4 } { 5 } ( x + 5 ) > \frac { 3 } { 5 } ( x + 5 )$ $Solve the inequality and draw a number line graph of the solution. - \frac { 4 } { 5 } ( x + 5 ) > \frac { 3 } { 5 } ( x + 5 )$

Solve the equation for y. -The temperature, t, in degrees Fahrenheit, of water being heated is $65 + \frac { 1 } { 4 } m$ where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

Solve the double inequality. - $- 38 \leq - 5 z + 2$ or $- 5 z + 2 \leq - 8$

Solve the equation. - $\frac { 1 } { 3 } ( 9 x - 15 ) = \frac { 1 } { 2 } ( 10 x - 6 )$

Solve the inequality and draw a number line graph of the solution. - $- 11 x - 12 \leq - 12 x - 16$ $Solve the inequality and draw a number line graph of the solution. - - 11 x - 12 \leq - 12 x - 16$

Solve the inequality graphically. Give the solution in interval notation. -Use the intersection method to solve $- 11 x - 8 \geq - 12 x - 6$ $Solve the inequality graphically. Give the solution in interval notation. -Use the intersection method to solve - 11 x - 8 \geq - 12 x - 6$

Find the zero of f(x). - $f ( x ) = 6 x + 12$

Construct a scatter plot of the data in the table. - x 20 23 -18 3 -23 -10 y -89 -43 32 -48 68 -8 $Construct a scatter plot of the data in the table. - \begin{array}{r|r|r|r|r|r|r} x & 20 & 23 & -18 & 3 & -23 & -10 \\ \hline y & -89 & -43 & 32 & -48 & 68 & -8 \end{array}$

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ . -

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if necessary. - x 10 20 30 40 50 y 3.9 4.6 5.4 6.9 8.3

Functions, Graphs, and Models; Linear Functions

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 2: Linear Models, Equations, and Inequalities

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear. - x 1 2 3 4 5 y 9 13 19 27 37

Solve the equation for y. - 6x−9y=16 x - 9 y = 16x−9y=1

Solve the system of equations by elimination, if a solution exists. - {6x−3y=−518x−9y=15\left\{ \begin{array} { l } 6 x - 3 y = - 5 \\18 x - 9 y = 15\end{array} \right.{6x−3y=−518x−9y=15​

Solve the inequality and draw a number line graph of the solution. - 45(x+5)>35(x+5)\frac { 4 } { 5 } ( x + 5 ) > \frac { 3 } { 5 } ( x + 5 )54​(x+5)>53​(x+5)

Solve the equation for y. -The temperature, t, in degrees Fahrenheit, of water being heated is 65+14m65 + \frac { 1 } { 4 } m65+41​m where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

Solve the double inequality. - −38≤−5z+2- 38 \leq - 5 z + 2−38≤−5z+2 or −5z+2≤−8- 5 z + 2 \leq - 8−5z+2≤−8

Solve the equation. - 13(9x−15)=12(10x−6)\frac { 1 } { 3 } ( 9 x - 15 ) = \frac { 1 } { 2 } ( 10 x - 6 )31​(9x−15)=21​(10x−6)

Solve the inequality and draw a number line graph of the solution. - −11x−12≤−12x−16- 11 x - 12 \leq - 12 x - 16−11x−12≤−12x−16

Solve the inequality graphically. Give the solution in interval notation. -Use the intersection method to solve −11x−8≥−12x−6- 11 x - 8 \geq - 12 x - 6−11x−8≥−12x−6

Find the zero of f(x). - f(x)=6x+12f ( x ) = 6 x + 12f(x)=6x+12

Construct a scatter plot of the data in the table. - x 20 23 -18 3 -23 -10 y -89 -43 32 -48 68 -8

The graph of a certain function y=f(x)y = f ( x )y=f(x) and the zero of that function is given. Using this graph, find a) the xxx -intercept of the graph of y=f(x)y = f ( x )y=f(x) and b) the solution to the equation f(x)=0f ( x ) = 0f(x)=0 . -