Question 1

Find the slope of the line containing the given points. $P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 )$

Accepted Answer

A)   4
B)    −12- \frac { 1 } { 2 }−21​ 
C)   0
D)   2
E)    12\frac { 1 } { 2 }21​ E

Question 2

Identify the steps needed to change the first inequality into the second. $2 y - x \geq 6 \text { to } y \geq \frac { 1 } { 2 } x + 3$

Accepted Answer

A)   Subtract x from both sidesDivide both sides by 2
B)   Subtract x from both sidesDivide both sides by 2 and reverse the inequality sign
C)   Add x to both sidesDivide both sides by 2 and reverse the inequality sign
D)   Add x to both sidesDivide both sides by 2
E)   Multiply both sides by  12\frac { 1 } { 2 }21​ D

Question 3

Find the x- and y-intercepts of the line 2x + 3y = 12 .

Accepted Answer

A)   (4, 0) , (0, 6) 
B)   (-6, 0) , (0, 4) 
C)   (6, 0) , (0, 4) 
D)   (4, 0) , (0, -6) 
E)   (6, 0) , (0, -4)  C

Question 4

Arrange slopes from flattest to steepest. $\frac { 7 } { 6 } , \frac { 6 } { 7 } , 1$

Accepted Answer

A)    76,67,1\frac { 7 } { 6 } , \frac { 6 } { 7 } , 167​,76​,1 
B)    67,76,1\frac { 6 } { 7 } , \frac { 7 } { 6 } , 176​,67​,1 
C)    1,76,671 , \frac { 7 } { 6 } , \frac { 6 } { 7 }1,67​,76​ 
D)    67,1,76\frac { 6 } { 7 } , 1 , \frac { 7 } { 6 }76​,1,67​ 
E)    76,1,67\frac { 7 } { 6 } , 1 , \frac { 6 } { 7 }67​,1,76​

Question 5

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left. $C = 95 + 0.15 ( d - 100 )$

Accepted Answer

A)   The slope is 80 and the vertical-axis intercept is 0.15.
B)   The slope is 0.15 and the vertical-axis intercept is 95.
C)   The slope is 0.25 and the vertical-axis intercept is 95.
D)   The slope is 0.15 and the vertical-axis intercept is 80.
E)   The slope is 90 and the vertical-axis intercept is 0.15.

Question 6

Find $g ( - 2 )$ and $g ( 3 )$ . $g ( x ) = 1 - x ^ { 2 }$

Accepted Answer

A)    555  ,  −6- 6−6 
B)    −3- 3−3  ,  −8- 8−8 
C)    333  ,  −11- 11−11 
D)    −1- 1−1  ,  −2- 2−2 
E)    −6- 6−6  ,  444

Question 7

Alberto earns a weekly salary of $500 plus 20% of his sales volume. Write an equation describing the total weekly earnings for x dollars in sales.

Accepted Answer

A)    y=20x+500y = 20 x + 500y=20x+500 
B)    y=500x+20y = 500 x + 20y=500x+20 
C)    y=0.2x+500y = 0.2 x + 500y=0.2x+500 
D)    y=−20x+500y = - 20 x + 500y=−20x+500 
E)    y=0.02x+500y = 0.02 x + 500y=0.02x+500

Question 8

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range). a. (7, 9), (7, 11), (7, 13)
b. (7, 9), (9, 11), (11, 13)

Accepted Answer

A)   b is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
B)   a is a function. Domain is {7}, range is {9, 11, 13}.
C)   a is a function. Domain is {7}, range is {9, 11, 13}.B is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
D)   b is a function. Domain is {7}, range is {9, 11, 13}.A is a function. Domain is {7, 9, 11}, range is {9, 11, 13}.
E)   a and b are not functions.

Question 9

Find the slope of the line containing the given points. $P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 )$

Accepted Answer

A)    38\frac { 3 } { 8 }83​ 
B)    14\frac { 1 } { 4 }41​ 
C)    −38- \frac { 3 } { 8 }−83​ 
D)   0
E)   undefined

Question 10

Given the function f(x) = 2x2 - 1, find $f ( - 3 )$

Accepted Answer

A)   17
B)   19
C)   -13
D)   21
E)   20

Question 11

Write an equation for the given data. slope = $\frac { 6 } { 7 } , y \text {-intercept } = - 5$

Accepted Answer

A)    y=67x+5y = \frac { 6 } { 7 } x + 5y=76​x+5 
B)    y=−5x+67y = - 5 x + \frac { 6 } { 7 }y=−5x+76​ 
C)    y=5x+67y = 5 x + \frac { 6 } { 7 }y=5x+76​ 
D)    y=−67x+5y = - \frac { 6 } { 7 } x + 5y=−76​x+5 
E)    y=67x−5y = \frac { 6 } { 7 } x - 5y=76​x−5

Question 12

Find x if f(x) = 0. $f ( x ) = 5 x - 2 ( x - 13 )$

Accepted Answer

A)    x=823x = 8 \frac { 2 } { 3 }x=832​ 
B)    x=713x = 7 \frac { 1 } { 3 }x=731​ 
C)    x=−713x = - 7 \frac { 1 } { 3 }x=−731​ 
D)    x=−823x = - 8 \frac { 2 } { 3 }x=−832​ 
E)    x=512x = 5 \frac { 1 } { 2 }x=521​

Question 13

A dieter limits a snack to 75 calories. What are three possible combinations of small carrots at 25 calories each and medium celery stalks at 3 calories each.

Accepted Answer

A)   The first combination: 1 carrot and 19 celery stalks.The second combination: 2 carrots and 8 celery stalks.The third combination: 3 carrots and 0 celery stalks.
B)   The first combination: 1 carrot and 16 celery stalks.The second combination: 2 carrots and 10 celery stalks.The third combination: 3 carrots and 0 celery stalks.
C)   The first combination: 1 carrot and 16 celery stalks.The second combination: 2 carrots and 8 celery stalks.The third combination: 3 carrots and 2 celery stalks.
D)   The first combination: 1 carrot and 19 celery stalks.The second combination: 2 carrots and 10 celery stalks.The third combination: 3 carrots and 2 celery stalks.
E)   The first combination: 1 carrot and 16 celery stalks.The second combination: 2 carrots and 8 celery stalks.The third combination: 3 carrots and 0 celery stalks.

Question 14

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is $\pi$ times diameter.

Accepted Answer

A)    C= circumference, d= diameter, C(d) =πd2C = 	ext { circumference, } d = 	ext { diameter, } C ( d )  = \pi d ^ { 2 }C= circumference, d= diameter, C(d) =πd2 
B)    C= circumference, d= diameter, C(d) =πdC = 	ext { circumference, } d = 	ext { diameter, } C ( d )  = \pi dC= circumference, d= diameter, C(d) =πd 
C)    C= circumference, d= diameter, C(d) =dπC = 	ext { circumference, } d = 	ext { diameter, } C ( d )  = \frac { d } { \pi }C= circumference, d= diameter, C(d) =πd​ 
D)    C= circumference, d= diameter, C(d) =π2dC = 	ext { circumference, } d = 	ext { diameter, } C ( d )  = \pi ^ { 2 } dC= circumference, d= diameter, C(d) =π2d 
E)    C= circumference, d= diameter, C(d) =πdC = 	ext { circumference, } d = 	ext { diameter, } C ( d )  = \frac { \pi } { d }C= circumference, d= diameter, C(d) =dπ​

Question 15

Which ordered pair is a solution to the inequality? $$y - \frac { 1 } { 2 } x \leq 2$$

Accepted Answer

A)   (4, 5) 
B)   (-4, 3) 
C)   (0, 5) 
D)   (7, 6) 
E)   (4, 0)

Question 16

Use the slope formula to find the slope. $( a , c )$ and $( b , c )$

Accepted Answer

A)    ba\frac { b } { a }ab​ 
B)   b
C)   0
D)   a
E)   undefined

Question 17

Given the function $s ( t ) = \frac { 3 } { 2 t - 1 }$ , find $s ( - 3 )$

Accepted Answer

A)    −37- \frac { 3 } { 7 }−73​ 
B)    333 
C)    37\frac { 3 } { 7 }73​ 
D)    −17- \frac { 1 } { 7 }−71​ 
E)    −35- \frac { 3 } { 5 }−53​

Question 18

Identify the steps needed to change the first inequality into the second. $3 x - 4 y > 12$ to $y < \frac { 3 x } { 4 } - 3$

Accepted Answer

A)   Subtract 3x from both sides.Divide both sides by -4 and reverse inequality sign.
B)   Subtract 3x from both sides.Divide both sides by 4 and reverse inequality sign.
C)   Add 4y to both sides.Divide both sides by -3 and reverse inequality sign.
D)   Add 4y to both sides.Divide both sides by 3 and reverse inequality sign.
E)   Add 4y to both sides.Divide both sides by 3.

Question 19

The output is the total cost of a shirt, where x is the price of the shirt and a sales tax of 9% of the price is added. Write an equation describing the output (y) as a function of the input (x).

Accepted Answer

A)    y=1.09xy = 1.09 xy=1.09x 
B)    y=x+0.09y = x + 0.09y=x+0.09 
C)    y=x−0.09y = x - 0.09y=x−0.09 
D)    y=0.91xy = 0.91 xy=0.91x 
E)    y=0.09x−1y = 0.09 x - 1y=0.09x−1

Question 20

Which ordered pair is a solution to the inequality? $$y \leq - 4$$

Accepted Answer

A)    (0,5) ( 0,5 ) (0,5)  
B)    (−4,5) ( - 4,5 ) (−4,5)  
C)    (0,−4) ( 0 , - 4 ) (0,−4)  
D)    (−4,6) ( - 4,6 ) (−4,6)  
E)    (0,6) ( 0,6 ) (0,6)

Exam 5: Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Find the slope of the line containing the given points. $P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 )$

Identify the steps needed to change the first inequality into the second. $2 y - x \geq 6 \text { to } y \geq \frac { 1 } { 2 } x + 3$

Find the x- and y-intercepts of the line 2x + 3y = 12 .

Arrange slopes from flattest to steepest. $\frac { 7 } { 6 } , \frac { 6 } { 7 } , 1$

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left. $C = 95 + 0.15 ( d - 100 )$

Find $g ( - 2 )$ and $g ( 3 )$ . $g ( x ) = 1 - x ^ { 2 }$

Alberto earns a weekly salary of $500 plus 20% of his sales volume. Write an equation describing the total weekly earnings for x dollars in sales.

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range) . a. (7, 9) , (7, 11) , (7, 13) b. (7, 9) , (9, 11) , (11, 13)

Find the slope of the line containing the given points. $P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 )$

Given the function f(x) = 2x² - 1, find $f ( - 3 )$

Write an equation for the given data. slope = $\frac { 6 } { 7 } , y \text {-intercept } = - 5$

Find x if f(x) = 0. $f ( x ) = 5 x - 2 ( x - 13 )$

A dieter limits a snack to 75 calories. What are three possible combinations of small carrots at 25 calories each and medium celery stalks at 3 calories each.

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is $\pi$ times diameter.

Which ordered pair is a solution to the inequality? $y - \frac { 1 } { 2 } x \leq 2$

Use the slope formula to find the slope. $( a , c )$ and $( b , c )$

Given the function $s ( t ) = \frac { 3 } { 2 t - 1 }$ , find $s ( - 3 )$

Identify the steps needed to change the first inequality into the second. $3 x - 4 y > 12$ to $y < \frac { 3 x } { 4 } - 3$

The output is the total cost of a shirt, where x is the price of the shirt and a sales tax of 9% of the price is added. Write an equation describing the output (y) as a function of the input (x) .

Which ordered pair is a solution to the inequality? $y \leq - 4$

Exam 5: Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Find the slope of the line containing the given points. P1(−2,−2) ,P2(2,0) P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 ) P1​(−2,−2) ,P2​(2,0)

Identify the steps needed to change the first inequality into the second. 2y−x≥6 to y≥12x+32 y - x \geq 6 \text { to } y \geq \frac { 1 } { 2 } x + 32y−x≥6 to y≥21​x+3

Find the x- and y-intercepts of the line 2x + 3y = 12 .

Arrange slopes from flattest to steepest. 76,67,1\frac { 7 } { 6 } , \frac { 6 } { 7 } , 167​,76​,1

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left. C=95+0.15(d−100) C = 95 + 0.15 ( d - 100 ) C=95+0.15(d−100)

Find g(−2) g ( - 2 ) g(−2) and g(3) g ( 3 ) g(3) . g(x) =1−x2g ( x ) = 1 - x ^ { 2 }g(x) =1−x2

Alberto earns a weekly salary of $500 plus 20% of his sales volume. Write an equation describing the total weekly earnings for x dollars in sales.

Which set of ordered pairs is a function? For each function, name the set of inputs (domain) and the set of outputs (range) . a. (7, 9) , (7, 11) , (7, 13) b. (7, 9) , (9, 11) , (11, 13)

Find the slope of the line containing the given points. P1(−8,1) ,P2(−8,−5) P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 ) P1​(−8,1) ,P2​(−8,−5)

Given the function f(x) = 2x2 - 1, find f(−3) f ( - 3 ) f(−3)

Write an equation for the given data. slope = 67,y-intercept =−5\frac { 6 } { 7 } , y \text {-intercept } = - 576​,y-intercept =−5

Find x if f(x) = 0. f(x) =5x−2(x−13) f ( x ) = 5 x - 2 ( x - 13 ) f(x) =5x−2(x−13)

A dieter limits a snack to 75 calories. What are three possible combinations of small carrots at 25 calories each and medium celery stalks at 3 calories each.

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is π\piπ times diameter.

Which ordered pair is a solution to the inequality? y−12x≤2y - \frac { 1 } { 2 } x \leq 2y−21​x≤2

Use the slope formula to find the slope. (a,c) ( a , c ) (a,c) and (b,c) ( b , c ) (b,c)

Given the function s(t) =32t−1s ( t ) = \frac { 3 } { 2 t - 1 }s(t) =2t−13​ , find s(−3) s ( - 3 ) s(−3)

Identify the steps needed to change the first inequality into the second. 3x−4y>123 x - 4 y > 123x−4y>12 to y<3x4−3y < \frac { 3 x } { 4 } - 3y<43x​−3

The output is the total cost of a shirt, where x is the price of the shirt and a sales tax of 9% of the price is added. Write an equation describing the output (y) as a function of the input (x) .

Which ordered pair is a solution to the inequality? y≤−4y \leq - 4y≤−4

Find the slope of the line containing the given points. $P _ { 1 } ( - 2 , - 2 ) , \quad P _ { 2 } ( 2,0 )$

Identify the steps needed to change the first inequality into the second. $2 y - x \geq 6 \text { to } y \geq \frac { 1 } { 2 } x + 3$

Arrange slopes from flattest to steepest. $\frac { 7 } { 6 } , \frac { 6 } { 7 } , 1$

Find the slope and the vertical-axis intercept for the equation. Assume that the output variable is on the left. $C = 95 + 0.15 ( d - 100 )$

Find $g ( - 2 )$ and $g ( 3 )$ . $g ( x ) = 1 - x ^ { 2 }$

Find the slope of the line containing the given points. $P _ { 1 } ( - 8,1 ) , \quad P _ { 2 } ( - 8 , - 5 )$

Given the function f(x) = 2x² - 1, find $f ( - 3 )$

Write an equation for the given data. slope = $\frac { 6 } { 7 } , y \text {-intercept } = - 5$

Find x if f(x) = 0. $f ( x ) = 5 x - 2 ( x - 13 )$

Define variables and write the sentence in function notation. The circumference of a circle is a function of the diameter. Circumference is $\pi$ times diameter.

Which ordered pair is a solution to the inequality? $y - \frac { 1 } { 2 } x \leq 2$

Use the slope formula to find the slope. $( a , c )$ and $( b , c )$

Given the function $s ( t ) = \frac { 3 } { 2 t - 1 }$ , find $s ( - 3 )$

Identify the steps needed to change the first inequality into the second. $3 x - 4 y > 12$ to $y < \frac { 3 x } { 4 } - 3$

Which ordered pair is a solution to the inequality? $y \leq - 4$