Algebra 1 Review - Linear Functions

Algebra 1 Review - Linear Functions

by Aimee Peralta

Multiple Choice

Solve for the variable in the equation:

8v - 4(v + 8) = 8

• 2
• 10
• 4
• -4 

Multiple Choice

Solve for the variable in the equation:

2x - 3 + 4x = 27

• 12
• 4
• 5
• 15

Multiple Choice

Solve for the variable k in the following equation:

7k − 1 − 6k = −6

• k = -2

• k = -3

• k = -4

• k = -5

Multiple Choice

Solve for x in the equation:

-8(-8x - 6) = -6x - 22

• 2/5
• -1
• 8/7 
• 2

Multiple Choice

Find the error in the problem below
19 - 2k = 3k - 1
     +3k   +3k
19 + 1k = -1
-19           -19
k = -20

• They should have divided by 1 for the last step
• They should add 19 instead of subtracting 19
• I can not find an error
• Instead of adding 3k they should subtract 3k

Multiple Choice

Solve for p
$A\ =\ \frac{1}{2}pa$

• $$A-\frac{1}{2}a\ =\ p$$

• $$\frac{2A}{a}=p$$

• $$\frac{A}{2a}=p$$

• $$2A-a\ =\ p$$

Multiple Choice

Solve for d
$C\ =\ \pi d$

• $$C\ -\ \pi=d$$

• $$C\ +\ \pi=d$$

• $$\pi C=d$$

• $$\frac{C}{\pi}=d$$

Multiple Choice

Solve for h
$V\ =\ lwh$

• $$V\ -l-w\ =\ h$$

• $$V-lw\ =\ h$$

• $$\frac{V}{lw}=\ h$$

• $$V-\frac{l}{w}=h$$

Multiple Choice

Solve for r:
$LA\ =\ 2\pi rh$

• $$LA-2\pi h\ =\ r$$

• $$\frac{LA}{2\pi h}=\ r$$

• $$\frac{LA}{2}-\pi h\ =\ r$$

• $$\frac{2LA}{\pi h}=\ r$$

Multiple Choice

Solve for x: $$m\ =\frac{x+y}{2}$$

• $$\ 2m-y=x$$

• $$\frac{2m}{y}=x$$

• $$\frac{m-y}{2}=x$$

• $$2\left(m-y\right)=x$$

Multiple Choice

r - 14 ≥ 17

• r ≥ 3
• r ≥ -31
• r ≥ 31
• r ≥ -3

Multiple Choice

x + 5 > 7

• x > -2
• x > 2
• x > 12
• x > -12

Multiple Choice

s + 9 ≥ -25

• s ≥ -18
• s ≥ -34
• s ≤ 18
• s ≥ 34

Multiple Choice

28 − k ≥ 7(k − 4)

• k ≥ -7
• k ≤ -7
• k ≥ 7
• k ≤ 7

Multiple Choice

6x + 2 + 6x < 14

• x < 1
• x > 1
• x < -1
• x > -1

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. The equation: C=2h+15. If Frank wants to rent the boat from to 3 to 6 hours, what is the domain and range?

• Domain: 3 < x < 6

  Range: 21 < y< 27

• Domain: 3 < x < 6

  Range: 21 < y < 27

• Domain: {3, 4, 5, 6}

  Range: { 21, 23, 25 , 27}

• Domain: { 21, 23, 25 , 27}

  Range: {3, 4, 5, 6}

Multiple Choice

A student is taking a test that has 20 questions on it. The student's score is a function of how many questions he misses: f(x)=100-5x, where x is the number of questions incorrect. If the student misses between 7 to 11 questions, What is the domain and range?

• Domain: {7, 8, 9, 10 ,11}

  Range: {65, 60 55, 50, 45}

• Domain: {7, 8, 9, 10 ,11}

  Range: {45, 50, 55, 60, 65}

• Domain: 7< x<11
  Range: 45<y< 65

• Domain: $$7\le x\le11$$
  Range: $$45\le y\le65$$

Multiple Choice

What is the domain of the graph shown?

• {-2, -1, 0, 1, 2, 3, 4}

• {2, 3, 4}

• 2 ≤ y ≤ 4

• -2 ≤ x ≤ 4

Multiple Choice

Give the range of the set of ordered pairs: (2, 11), (9, -3), (7, 21), (-8, 6)

• {2, 9, 7, -8}

• {-3, 6, 11, 21}

• -8 < x < 9

• -3 < y < 21

Multiple Choice

What is the Domain of the situation?

• $$0\le x\ \le9$$  

• $$0<x<9$$  

• $$0<x<28$$  
  

• $$0\le y\le28$$

Multiple Choice

A pizza shop sells pizza for $7.50 each plus $1.25 per topping. The total price of the pizzas can be determined by the function P(t) = 7.5 + 1.25t, where te is the number of toppings orders and P(t) is the total price of the pizza. If the shop has a delivery policy that all orders must have a minimum of 2 toppings and maximum of 8 toppings for a delivery, what is the range

• {10, 11.25, 12.50, 13.75, 15, 16.25, 17.50}

• {2, 3, 4, 5, 6, 7, 8}

• 10 ≤ P(t) ≤ 17.50

• 0 ≤ P(t) ≤ 17.50

Multiple Choice

The total cost in dollars to buy uniforms for the players on the volleyball team can be found using the function c = 34.95u + 6.25, where u is the number of uniforms bought.  If there are at least 8 players but not more than 12 players on team, what is the domain of the situation?

• 0 < u ≤ 12
• 0 < c ≤ 425.65
• {8, 9, 10, 11, 12}
• {295.85, 320.80, 355.75, 390.70, 425.65}

Multiple Choice

What is the domain of a relation?

• the set of all x-values

• the set of all y-values

Multiple Choice

Which is the set of all y-values or the outputs?

• Domain

• Range

• Relation

• Function

Multiple Choice

What is the range of the table?

• {-4, 0, 1, 3}

• {-2, 0, 2, 3}

• {-4, -2, 0, 1, 2, 3}

• { (0, 0), (2, -4), (3, 3), (-2, 1) }

Multiple Choice

What is the domain?

• {-2, -1, 0, 1, 8}
• {3, 5, 7 , 9, 0}
• {-2, -1, 0, 1, 3, 5, 7, 8, 9}
• {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Multiple Choice

What is the domain?

• all real numbers
• 1<x<6
• {1,3,4,6}
• {-2,2,5}

Multiple Choice

What is the range?

• {-2,2,5}
• {1,3,5,6}
• all real numbers 
• -2<y<5

Multiple Choice

Describe the correlation in the graph shown.

• Negative correlation
• Positive correlation
• No correlation
• cannot be determined

Multiple Choice

What is the Range of the situation?

• $$0\le x\ \le9$$  

• $$0<x<9$$  

• $$0<x<28$$  
  

• $$0\le y\le28$$

Multiple Choice

f(x) = −2x − 12

f(−5) = ?

• −22

• −2

• −19

• −5

Multiple Choice

Consider the function: f(x) = x + 3

For which value of x does f(x) = −5?

(Hint: Find which x can be substituted into the function that gives an answer of -5.)

• −2

• −1

• −8

• 7

Multiple Choice

Consider the function: f(x) = 2x + 2

For which value of x does f(x) = 2?

(Hint: Determine which value can be substituted in for x to get a solution of 2.)

• 6

• −8

• 10

• 0

Multiple Choice

f(x) = −2x + 13

f(10) = ?

• −7

• 1

• −8

• 7

Fill in the Blank

g(x) = 5 − 6x

g(−5) = ?

Fill in the Blank

f(x) = 4x + 5

f(4) = ?

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• x

Multiple Choice

What is the y-intercept in the following equation:  y=-4x-5

• -4
• -4x
• 5
• -5

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3
• y=2/3-3
• y=2/3x-3
• y=2/3x+3

Multiple Choice

Write the equation for the line in slope-intercept form.

• y= -1x+3
• y= 4x+3
• y=1/4x+3
• y= -4x+3

Multiple Choice

Write the equation of the line.

• y= -1x-3
• y= -3x-1
• y=-1/3x-1
• y= -3x-3

Multiple Choice

• m = 1/2
• m = 1/3
• m = 2
• m = (0, 1)

Multiple Choice

• m = 5/0
• m = -2/3
• m = 2/3
• m = 3/2

Multiple Choice

Write the equation in slope-intercept form (solve for y):
2y = 10x + 14

• y = 10x + 12
• y = 10x + 7
• y = 5x + 14
• y = 5x + 7

Multiple Choice

Write the equation in slope-intercept form (solve for y):

y + 4 = 8x

• y = 2x

• y = 8x - 4

• y = 2x

• y = 8x + 4

Multiple Choice

What is the slope of the line through the points (2, 4) and (2, -11)?

• m = 0
• m = -15/0
• m = 13/2
• m is undefined

Multiple Choice

Find the slope

• -2/3
• 3/2
• -3/2
• 2/3

Multiple Choice

What is the slope?

• 2
• 1/2
• 1
• 1.5

Multiple Choice

Find the slope of the line that passes through
(10, 1) and (5, 2)

• 1/5
• -1/5
• 5
• -5

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

y = 5/7x +2
y = 5/7x - 30
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

y = 6x + 2
y = -6x + 2
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

A line is perpendicular to    y = 2x - 7.
What is the slope of this line? 

• -2
• 1/2
• -1/2
• 2

Multiple Choice

What is the slope of a line parallel to y = -2/6x + 10

• 2/6

• -1/3

• 6/2

• -3

Multiple Choice

• The graph of g(x) is a horizontal stretch of the graph of f(x)

• The graph of g(x) is a horizontal shrink of the graph of f(x)
  

• The graph of g(x) is a vertical stretch of the graph of f(x)

• The graph of g(x) is a vertical shrink of the graph of f(x)

Multiple Choice

• The graph of g(x) is a horizontal stretch of the graph of f(x)

• The graph of g(x) is a horizontal shrink of the graph of f(x)
  

• The graph of g(x) is a vertical stretch of the graph of f(x)

• The graph of g(x) is a vertical shrink of the graph of f(x)

Multiple Choice

• The graph of g(x) is a reflection in the x-axis of the graph of f(x)

• The graph of g(x) is a reflection in the y-axis of the graph of f(x)
  

Multiple Choice

• The graph of g(x) is a reflection in the x-axis of the graph of f(x)

• The graph of g(x) is a reflection in the y-axis of the graph of f(x)
  

Multiple Choice

f(x) = 3x-2, g(x)=f(x+3)

• The graph of g(x) is a vertical translation of 3 units down of the graph of of f(x)

• The graph of g(x) is a vertical translation of 3 units up of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units left of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units right of the graph of of f(x)

Multiple Choice

f(x) = x/3 - 3, g(x) = f(x) + 3

• The graph of g(x) is a vertical translation of 3 units down of the graph of of f(x)

• The graph of g(x) is a vertical translation of 3 units up of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units left of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units right of the graph of of f(x)

Multiple Choice

f(x) = -2x+1, g(x) = f(x) - 3

• The graph of g(x) is a vertical translation of 3 units down of the graph of of f(x)

• The graph of g(x) is a vertical translation of 3 units up of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units left of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units right of the graph of of f(x)

Multiple Choice

f(x) = -x/4+2, g(x) = f(x-3)

• The graph of g(x) is a vertical translation of 3 units down of the graph of of f(x)

• The graph of g(x) is a vertical translation of 3 units up of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units left of the graph of of f(x)

• The graph of g(x) is a horizontal translation of 3 units right of the graph of of f(x)

Multiple Choice

• The graph of g(x) is a horizontal stretch of the graph of f(x)

• The graph of g(x) is a horizontal shrink of the graph of f(x)
  

• The graph of g(x) is a vertical stretch of the graph of f(x)

• The graph of g(x) is a vertical shrink of the graph of f(x)

Multiple Choice

• The graph of g(x) is a horizontal stretch of the graph of f(x)

• The graph of g(x) is a horizontal shrink of the graph of f(x)
  

• The graph of g(x) is a vertical stretch of the graph of f(x)

• The graph of g(x) is a vertical shrink of the graph of f(x)

Multiple Choice

What is a scatter plot?

• A graph that shows the relationship of two data sets.
• A graph drawn using rectangular bars to show how large each value is.
• A graph that shows information that is connected in some way.
• A graph that shows data changing over time.

Multiple Choice

Which scatter plot shows a linear relationship between x and y?

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit?

• The more books students read, the lower their English grade.
• The more books students read, the higher their English grade.
• The fewer books students read, the higher their English grade. 
• No relationship exists between the number of books students read and their English grades. 

Multiple Choice

What is the correlation between length of running start and distance of jump?

• positive:  the further you run the further you jump
• negative: the less you run the less distance of your jump
• positive: the further your running start the less your distance

Multiple Choice

Which best describes the form of this scatterplot?

• linear
• nonlinear
• scattered

Multiple Choice

What is the type of correlation?

• Negative 
• no correlation
• positive 

Multiple Choice

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

• y = 1.5x + 12

• y = 12x + 1.5

• y = 0.67x - 8

• y = -8x + 0.67

Multiple Choice

A person travels by car.  They record their miles driven in a data table.  Calculate the linear regression equation of this data.

• y = 61.93x - 1.79
• y = -1.79x + 61.93
• y = 0.016x + 0.03
• y = 0.03x + 0.016

Multiple Choice

The annual profits for a company are given in the following table, where x represents the number of years since 1992, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the year in which the profits would reach 378 thousand dollars.

• 2029

• 2014

• 2003

• 8753

Multiple Choice

The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 1994, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected number of new cases for 2003, rounded to the nearest whole number.

• 974

• 25,101

• 940

• 952

Multiple Choice

What is the line of best fit?

• f(x)= 5x+1.82
• cannot be determined
• f(x)= 1.82x + 5.02
• f(x)= 1.1x + 4.2

Multiple Choice

Using your linear regression, what is y when x is 30?

• 61.59
• 52.46
• 57.94
• 59.76

Multiple Choice

• 5,000
• 2,620
• 17,000
• 20,200

Multiple Choice

In a direct variation, y = 39 when x = 3. 
Find the value of y when x = 2.

• 26
• 3
• 58.5
• 2

Multiple Choice

The value of y varies directly with x.  Which function represents the relationship between x and y if y = 14 when x = 6. 

• y=20x
• y=84x
• y=7/3x
• y=3/7x

Multiple Choice

If x and y vary directly, what is the missing value in the points (x, 4) and (-14, -8)?

• x = -7
• x = -2.3
• x = 2.3
• x = 7

Multiple Choice

The amount of money earned on a job is directly proportional to the number of hours worked.  If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

• $2
• $308
• $1.57
• $265

Multiple Choice

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours? 

• $394
• $440
• $472.80
• $512.20

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Multiple Choice

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution. 
• you will have one solution.
• you will have infinite solutions. 
• you will graph a giraffe. 

Multiple Choice

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

Multiple Choice

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x
• The  y
• The  z
• The unknown

Multiple Choice

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Multiple Choice

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  Player one rushed for 4 times as many yards as player two. How many yards did each player rush for? 

• Player one 1240 yards, Player two 310
• Player one 310 yards, Player two 1240
• Player one 1000 yards, Player two 550
• Player one 550 yards, Player two 1000

Multiple Choice

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  How many nickels and dimes did Dennis earn? 

• 40 nickels, 40 dimes
• 52 nickels, 28 dimes
• 28 nickels, 52 dimes
• 30 nickels, 50 dimes

Multiple Choice

Which inequality is graphed on the given coordinate plane?

•  y > x + 1
• y < x + 1
• y ≥ -x + 1
• y ≤ -x + 1

Multiple Choice

Which ordered pair(s) is a solution to the given system?

• (5, -5)
• (0,0)
• (-5, -2)
• (3,-3)

Multiple Choice

This system has an infinite number of solutions, TRUE or FALSE?

• TRUE
• FALSE

Multiple Choice

Which system of linear inequalities is represented by the graph?

• y≤2x-1
  y>-2x+3
• y>2x-1
  y≤-2x+3
• y<2x-1
  y≥-2x+3
• y≤2x-1
  y>2x+3

Multiple Choice

The 30 members of a choir are trying to raise at least $1,500 to cover travel costs to a singing camp. They have already raised $600. Which inequality could you solve to find the average amounts each member can raise that will at least meet the goal?

• 30x + 600 > 1,500
• 30x + 600 ≥ 1,500
• 30x + 600 < 1,500
• 30x + 600 < 1,500

Multiple Choice

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

• x + y ≥ 6
  32x + 20y ≤ 150

• x + y ≥ 632
  x + 20y ≥ 150

• x + y ≤ 6
  32x + 20y ≤ 150

• x + y ≤ 6
  32x + 20y ≥ 150

Multiple Choice

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40