Free Printable linear functions

1.

Which equation is being represented by this line?

a)

y = -1x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

2.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

3.

Find the slope of the line.

a)

3/2

b)

-43/2

c)

2

d)

-2

4.

Find the slope of the line.

a)

Undefined

b)

0

c)

1/1

d)

-1/1

5.

Which equation represents the graph?

a)

x = 2

b)

y = 2

c)

y = 2x

d)

y = undefined

6.

Graph

a)

b)

c)

d)

7.

Y-intercept is where the line ______________.

a)

begins

b)

crosses the x-axis

c)

crosses the y-axis

d)

ends

8.

When you graph a line using slope-intercept form, you plot the ___________ first and then the ___________.

a)

origin; slope

b)

slope; y-intercept

c)

y-intercept; x-intercept

d)

y-intercept; slope

9.

Which equation matches the graph?

a)

y = 2x

b)

y = 1/4 x + 2

c)

y = 1x + 4

d)

y = -2x

10.

Write the equation of the line.

a)

y= -1x-3

b)

y= -3x-1

c)

y=(-1/3)x-1

d)

y= -3x-3

11.

A line has slope m=3/4 and passes through the point (0,-5) what is the equation of the line?

(a)

12.

A line has slope m=3 and passes through the point (2,1). What is the equation of the line?

(a)

13.

Write an equation of the line through the points (-2, -2) and (4,1).

(a)

14.

Write an equation of the line through the points (2,4) and (1,-2).

(a)

15.

Given that the slope is -4 and the y intercept is -4 what is the equation of the line?

a)

y = 4x - 4

b)

y = -4x - 4

c)

y = -4

d)

y = -4x + 4

16.

Which of these is a graph of a linear function?

a)

b)

c)

d)

17.

What is the slope of a line between (-4,14) and (-16,8)? Reminder!

Formula:

$m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$

(a)

18.

Calculate the slope of a line that passes through these points. (1,3)(-1,7)

a)

-2

b)

2

c)

-5

d)

-1/2

19.

Which of these is point-slope?

a)

$y-y_1=m\left(x-x_1\right)$

b)

$y=mx+b$

c)

$Ax+By=C$

20.

Write an equation of the line going through the point (-4, 1) with a slope of 1/3.

a)

$y-1=\frac{1}{3}\left(x+4\right)$

b)

$y+4=\frac{1}{3}\left(x-1\right)$

c)

$y-4=\frac{1}{3}\left(x+1\right)$

d)

$y+1=\frac{1}{3}\left(x-4\right)$

21.

Name the slope of this line:

$y+1=-\frac{5}{4}\left(x-3\right)$

(a)

22.

Name the point given in this line: $y+1=-\frac{5}{4}\left(x-3\right)$

(a)

23.

Write the equation in point-slope form for the line that contains the points

(-2, -3), (4, 3)

a)

y - 3 = 1(x - 2)

b)

y + 3 = 1(x + 2)

c)

y -3 = -1(x + 2)

d)

y + 3 = -1(x - 2)

24.

Is this slope intercept form?

2y\ =4x\ +10

a)

yes because it's $y=mx+b$

b)

no, because there is a coefficient on the y. You need to divide the entire equation by 2 first in order to get $y=mx+b$

25.

Transform this point-slope equation into slope intercept form:

$y-2=3\left(x+4\right)$

(a)

26.

Select the equation represents a line with a slope of 8

that passes through the point $\left(2,7\right)$

a)

$y-8=2\left(x-7\right)$

b)

$y-7=8\left(x-2\right)$

c)

$y+7=8\left(x+2\right)$

27.

What is the formula for standard form?

a)

y=mx+b

b)

$y-y_1=m\left(x-x_1\right)$

c)

$Ax+By=C$

d)

$\frac{rise}{run}$

28.

Which equation is written in STANDARD form?

a)

y=\frac{1}{2}x+2

b)

$y-3=-5\left(x+2\right)$

c)

$-7x+2y=9$

d)

$3x+2=y$

29.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

30.

What is the y-intercept of

2x-5y=35

?

a)

$\left(0,-7\right)$

b)

$\left(-7,0\right)$

c)

$\left(\frac{35}{2},0\right)$

d)

$\left(0,\frac{35}{2}\right)$

31.

Which graph represents 2x + 4y = 12?

a)

b)

c)

d)

32.

Write the slope intercept form of the equation 3x - 2y = -16

a)

y = -3x - 8

b)

y = -3x + 8

c)

y = -3/2x - 8

d)

y = 3/2 x + 8

33.

What is the slope-intercept form of a line?

a)

Ax + By = C

b)

y = mx + b

c)

y - y1 = m(x - x1)

d)

y = Ax + By

34.

In which form is the following linear function?

4x+2y=8

a)

Slope Intercept Form

b)

Point-Slope Form

c)

Standard Form

35.

In which form is the following linear function?

y=-\frac{1}{2}x+2

a)

Slope Intercept Form

b)

Point-Slope Form

c)

Standard Form

36.

Graph

a)

b)

c)

d)

37.

What is the domain restriction of the blue piece of this function?

a)

x > 0

b)

x ≥ 0

c)

x > 2

d)

x ≥ 2

38.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

39.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

40.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

41.

Graph

a)

b)

c)

d)

42.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

43.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

44.

What is the domain interval for the green piece of this function?

a)

-2 < x ≤ 1

b)

-1 < x ≤ 0.5

c)

x > -2

d)

x ≤ 1

45.

Evaluate f(0)

a)

0

b)

19

c)

9

d)

-19

46.

How many pieces is this Piecewise Function composed of?

a)

1

b)

2

c)

3

d)

4

47.

Functions that are made up of distinct "pieces" of other functions defined over different intervals are called

a)

Absolute Value Functions

b)

Piecewise Functions

c)

Exponential Functions

d)

Quadratic Functions

48.

The first three terms of an arithmetic sequence are as follows

13, 19, 25

What are the next two terms of the sequence?

a)

31 and 37

b)

31 and 36

c)

30 and 37

d)

30 and 36

49.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

50.

Which sequence is NOT an arithmetic sequence?

a)

12, 18, 24, 30,...

b)

10, 3, -4, -11,...

c)

2, 4, 8, 16,...

d)

16, 20, 24, 28,...

51.

What is the common difference of the sequence 2, -1, -4, -7,...?

a)

-3

b)

-1

c)

-2

d)

3

52.

An arithmetic sequence is given below.

2, 9, 16, 23, ...

Which is the explicit formula for the n^th term a_n?

a)

a_n= -7n+9

b)

a_n= 7n-5

c)

a_n= 7n-9

d)

a_n= -7n+5

53.

An arithmetic sequence is given below.

16, 13, 10, 7, ...

Which is the explicit formula for the n^th term a_n?

a)

a_n= -3n+19

b)

a_n= -5n+13

c)

a_n= 3n+13

d)

a_n= -5n+20

54.

What is the 67^th term of the following arithmetic sequence.

13, 22, 31, 40, ...

a)

-445

b)

67

c)

625

d)

607

55.

What is the 76^th term of the following arithmetic sequence?

8, 14, 20, 26,...

a)

76

b)

452

c)

458

d)

476

56.

What is the common difference of the following sequence?

7, 27, 47, 67,...

a)

10

b)

20

c)

3

d)

-20

57.

What is a₁ in the following sequence?

-6, -14, -22, -30, ...

a)

-6

b)

-14

c)

-22

d)

-30

58.

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=2+6n

b)

a_n=-6+6n

c)

a_n=6n-4

d)

a_n=4-6n

59.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

60.

Define arithmetic sequences.

a)

A sequence whose terms change by adding the same number each time.

b)

A sequence whose terms change by multiplying the same number each time.

c)

A sequence whose terms change by dividing the same number each time.

d)

A list of numbers that often (but not always) form a pattern.

61.

Define common difference.

a)

the product between two consecutive terms of a geometric sequence.

b)

the product between two consecutive terms of an arithmetic sequence.

c)

the difference between two consecutive terms of an arithmetic sequence.

d)

the difference between two consecutive terms of a geometric sequence.

62.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

63.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

a)

-16, -21, -26, -31

b)

5, -11, -27, -43

c)

-16, -80, -500, -200

d)

-16, -11, -6, -1

64.

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

a)

a_n = a_n-1 + 16
a₁=17

b)

a_n = a_n-1 - 17
a₁=17

c)

a_n = a_n-1 - 15
a₁=17

d)

a_n = a_n-1 - 16
a₁=17

65.

Find the common difference.

a)

$d=4$

b)

$d=6$

c)

$d=8$

d)

$d=5$

66.

Find the common difference.

a)

$d=-3$

b)

$d=3$

c)

$d=-2$

d)

$d=-4$

67.

Find the first five terms.

a)

$-8,-17,-26,-35,-44$

b)

$-18,-26,-34,-42,-50$

c)

$-18,-28,-38,-48,-58$

d)

$-8,-18,-28,-38,-48$

68.

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=2+6n

b)

a_n=-6+6n

c)

a_n=6n-4

d)

a_n=4-6n

69.

Find the explicit formula:
-3, -33, -63, -93, ...

a)

a_n = -3 - 30(n -1)

b)

a_n = -3 + 30(n -1)

c)

a_n = -30 - 3(n -1)

d)

a_n = -30 + 3(n -1)

70.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence. (Hint: Simplify your equation.)

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

71.

What is the 15th term of the sequence an = -3n+50

a)

95

b)

-5

c)

5

d)

-95

72.

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

NOTE: a_n = output (y) and n = input (x)

a)

a_n= 10n + 17

b)

a_n = 7n - 17

c)

a_n = -7n + 17

d)

a_n = 7n + 3

73.

Write the explicit rule for the arithmetic sequence 12, 10, 8, 6, ...

NOTE: a_n = output (y) and n = input (x)

a)

a_n = 12n - 14

b)

a_n= 2n - 14

c)

a_n= -2n + 14

d)

a_n= -12n + 14

74.

Match each variable from the Arithmetic Formula with its definition.

a)

a₁

1.

1st Term

b)

d

2.

Common Difference

c)

a_n

3.

Nth Term

d)

n

4.

Order/Position of Term

75.

Which variable from the Arithmetic Sequence is NOT seen in the Slope-Intercept form of the same equation?

a)

a₁

b)

d

c)

a_n

d)

n

76.

In recursive formulas what does the term a_n-1represent?

a)

the previous term

b)

the term you are looking for

c)

the first term

d)

the last term

77.

In recursive formulas what does the term a₁ represent?

a)

the previous term

b)

the term you are looking for

c)

the first term

d)

the last term

78.

Use the explicit formula to find the 7th term of the sequence.
$a_n=22-3\left(n-1\right)$

a)

4

b)

1

c)

18

d)

114

79.

Write the explicit formula for the sequence.

10, -2, -14, -26, ...

a)

$a_n=10\cdot\left(-\frac{1}{5}\right)^{\left(n-1\right)}$

b)

$a_n=-2\cdot7^{\left(n-1\right)}$

c)

$a_n=10-8\left(n-1\right)$

d)

$a_n=10-12\left(n-1\right)$

80.

Now, let's go backwards!!! Given the explicit formula, what is the first term?

$a_n\ =\ 3\ +\ \left(n\ -\ 1\right)\left(2\right)$

(a)

81.

Now, let's go backwards!!! Given the explicit formula, list the first five terms in order.

$a_n\ =\ 3\ +\ \left(n\ -\ 1\right)\left(2\right)$

a)

2, 5, 8, 11, 14, ...

b)

3, 1, -1, -3, -5, ...

c)

3, 6, 9, 12, 15, ...

d)

3, 5, 7, 9, 11, ...

82.

Now, let's go backwards!!! Given the explicit formula, list the first five terms in order. (You can ignore term 0)

$a_n\ =\ 1+2n$

a)

2, 5, 8, 11, 14, ...

b)

3, 1, -1, -3, -5, ...

c)

3, 6, 9, 12, 15, ...

d)

3, 5, 7, 9, 11, ...

83.

TRUE or FALSE?

An arithmetic sequence is an example of a linear function.

a)

True, because having a common difference also means it has a constant rate of change

b)

False, because it's not shown on a graph

84.

In his piggy bank, Bingo dropped $1.00 on May 1, $1.75 on May 2, $2.50 on May 3 and so on until the last day of May. How much did he drop in his piggy bank on May 19?

a)

$13.50

b)

$13.75

c)

$14.50

d)

$15.25

85.

A well is dug 800 meters deep. The 1^st meter costs $250 and the cost per meter increases by $50 for every subsequent meter. Find the cost of digging the 750^th meter.

a)

$37,700

b)

$37,750

c)

$36,650

d)

$13,300

86.

After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day?

a)

9 weeks

b)

8 weeks

c)

366 weeks

d)

372 weeks

87.

There are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third carriage, and so on in an arithmetic sequence. What is the total number of passengers in the 7th carriage?

a)

225

b)

250

c)

275

d)

300

88.

Bricks are stacked in a pile with 24 bricks on the bottom row and 15 on the top row with each row having one more brick than the one above it. How many rows are there in all?

a)

7

b)

8

c)

9

d)

10

89.

Find 141st term of the arithmetic sequence: 15, 13, 11, 9...

1) Use the formula $a_n=a_1+\left(n-1\right)\left(d\right)$

2. Replace $n$ with the term you are looking for ( $141$ )

3. Replace $a_1$ with the first tern in the arithmetic sequence ( $15$ )

4. Say to yourself, this is why I was told to have a calculator ;)

5. The 141st term of the arithmetic sequence is (a)

90.

Select all that are true about arithmetic sequences

a)

They are a type of linear function

b)

$t\left(n\right)\ =\ b\left(g\right)^n$

Their equations look like

c)

Their graphs are dots in a straight line

d)

Their graphs are curved

91.

Fill in the blanks: Arithmetic sequences are graphed as _________ functions.

a)

Linear

b)

Exponential

92.

Identify the first term of this sequence.

a)

0

b)

1

c)

2

d)

3

93.

Find the explicit formula for the sequence shown in the graph.

a)

$a_n=2\left(3\right)^{\left(n-1\right)}$

b)

$a_n=3+2\left(n-1\right)$

c)

$a_n=2+3\left(n-1\right)$

d)

$a_n=2+5\left(n-1\right)$

94.

Simplify the explicit formula for the sequence shown in the graph so that it is in function form.

a)

$f\left(n\right)=3+2n$

b)

$f\left(n\right)=-1+3n$

c)

$f\left(n\right)=2+3n$

d)

$f\left(n\right)=5+3n$

95.

Find the explicit formula for the sequence shown in the graph.

a)

$a_n=20-14\left(n-1\right)$

b)

$a_n=20-6\left(n-1\right)$

c)

$a_n=6-20\left(n-1\right)$

d)

$a_n=20+6\left(n-1\right)$

96.

There are 120 gallons of water in a tank. Each minute it releases 25 gallons. Write the arithmetic rule and determine how much water is in the tank at 4 minutes.

a)

y = 25x + 95

195 gallons

b)

y = -25x + 145

45 gallons

c)

y = 25x + 120

245 gallons

d)

y = -25x + 120

20 gallons

97.

What does d represent?

a)

any term

b)

first term

c)

common difference

d)

term number

98.

What does n represent?

a)

any term

b)

first term

c)

common difference

d)

term number

99.

Which graph matches the arithmetic sequence:

a_n= 15 -5(n-1)

a)

b)

c)

d)

100.

Which graph matches the arithmetic sequence:

a_n= -4 +3(n-1)

a)

b)

c)

d)

linear functions

Total questions: 100

Worksheet time: 2hrs 40mins

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