Patterns and Functions: Master the Art of Recognizing and Extending Patterns

Question 1

What is the next number in the sequence: 2, 4, 6, 8, ...?

Accepted Answer

10

Answer

9

Answer

12

Question 2

What is the missing number in the table below?
|n|Value|
|---|---| 
|1|5|
|2|10|
|3|15|
|4|?|

Accepted Answer

20

Answer

15

Answer

25

Question 3

Which of the following equations represents the line that has a slope of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = 2x + 1

Answer

y = -2x - 1

Question 4

What is the independent variable in the relationship between the height of a plant and the amount of sunlight it receives?

Accepted Answer

Amount of sunlight

Answer

Height of the plant

Answer

Time

Question 5

Which of the following is NOT a type of numerical pattern?

Accepted Answer

Algebraic

Answer

Arithmetic

Answer

Geometric

Answer

Periodic

Question 6

A table of values shows a relationship between two variables. Which of the following is NOT a way to represent this relationship?

Accepted Answer

Bar Chart

Answer

Graph

Answer

Equation

Answer

Scatter Plot

Question 7

Which of the following graphs represents a relationship where the dependent variable increases at a constant rate as the independent variable increases?

Accepted Answer

A straight line

Answer

A parabola

Answer

A circle

Answer

A hyperbola

Question 8

Which of these is NOT a type of pattern?

Accepted Answer

Random

Answer

Arithmetic

Answer

Geometric

Answer

Fibonacci

Question 9

The following table shows the relationship between the number of hours worked and the amount earned. Which equation best represents this relationship?

Accepted Answer

y = 2x

Answer

y = 2x + 1

Answer

y = x/2

Answer

y = x/2 + 1

Question 10

What is the y-intercept of the line y = 2x - 1?

Accepted Answer

-1

Answer

1

Answer

2

Answer

-2

Question 11

What is the domain of the function f(x) = 1/(x - 2)?

Accepted Answer

All real numbers except for 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All negative real numbers

Question 12

Which of these is NOT a type of pattern?

Accepted Answer

Random

Answer

Arithmetic

Answer

Geometric

Answer

Proportional

Question 13

Which of the following statements is true about the pattern: 2, 4, 8, 16, 32, ...?

Accepted Answer

It is a geometric pattern with a common ratio of 2.

Answer

It is an arithmetic pattern with a common difference of 2.

Answer

It is a quadratic pattern.

Answer

It is a random pattern.

Question 14

What is the slope of the line represented by the equation y = 3x - 2?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 15

In the function y = 3x – 5, which variable is the independent variable?

Accepted Answer

x

Answer

y

Answer

-5

Answer

3

Question 16

Which equation represents the relationship between the number of hours worked (x) and the amount earned (y) if the pay rate is $10 per hour?

Accepted Answer

y = 10x

Answer

y = x/10

Answer

y = 10 – x

Answer

y = x + 10

Question 17

Find the y-intercept of the line represented by the equation 3x + 2y = 12.

Accepted Answer

4

Answer

6

Answer

12

Question 18

Which of the following shows a set of numbers arranged in a predictable pattern?

Accepted Answer

1, 3, 5, 7, 9

Answer

1, 2, 3, 4, 5

Answer

Red, blue, yellow, red, blue, yellow

Answer

A, B, C, D, E

Question 19

Which of these equations matches the given pairs of values: (1, 3), (2, 5), (3, 7)? The equation should show a linear relationship between x and y.

Accepted Answer

y = 2x + 1

Answer

y = x + 2

Answer

y = 3x - 1

Answer

y = x - 3

Question 20

Which expression shows a relationship where the output (y) stays the same no matter what the input (x) is?

Accepted Answer

y = 3

Answer

y = x + 2

Answer

y = 2x

Answer

y = x^2

Question 21

In the equation y = 2x - 4, what is the y-intercept?

Accepted Answer

-4

Answer

-2

Answer

2

Answer

4

Question 22

For the function f(x) = 2x + 1, what are the possible values for x?

Accepted Answer

All real numbers

Answer

All positive numbers

Answer

All integers

Answer

All rational numbers

Question 23

Which option is NOT a way to express a pattern?

Accepted Answer

Story

Answer

Table

Answer

Graph

Answer

Equation

Question 24

What is the next number in the pattern: 2, 4, 8, 16, ...?

Accepted Answer

32

Answer

24

Answer

48

Answer

64

Question 25

Which pattern is a geometric progression?

Accepted Answer

1, 2, 4, 8, 16

Answer

1, 3, 5, 7, 9

Answer

2, 4, 6, 8, 10

Answer

2, 3, 5, 8, 12

Question 26

Which number is a valid input for the function f(x) = 2x - 5?

Accepted Answer

any number

Answer

0

Answer

1

Answer

-1

Question 27

What is the output of the function g(x) = x^2 + 1 when x = 3?

Accepted Answer

13

Answer

10

Answer

-8

Answer

1

Question 28

Which expression will shift the graph of f(x) = x up by 2 units?

Accepted Answer

f(x) = x + 2

Answer

f(x) = -x

Answer

f(x) = x^2

Answer

f(x) = 1/x

Question 29

What is the domain of the function h(x) = √(x - 2)?

Accepted Answer

[2, ∞)

Answer

[0, ∞)

Answer

(-∞, ∞)

Answer

(-2, ∞)

Question 30

Which of these is NOT a type of pattern?

Accepted Answer

Random

Answer

Numeric

Answer

Algebraic

Answer

Geometric

Question 31

The sequence of numbers 1, 3, 9, 27, 81, ... is generated by a rule. What is that rule?

Accepted Answer

Multiply by 3

Answer

Multiply by 4

Answer

Multiply by 5

Answer

Multiply by 6

Question 32

Which of these is the definition of a function?

Accepted Answer

A set of ordered pairs where each first element has only one second element paired with it

Answer

A relation where each second element has only one first element paired with it

Answer

A collection of ordered pairs where each first element may have multiple second elements paired with it

Answer

A set of pairs where each second element may have multiple first elements paired with it

Question 33

The graph of a function is a straight line. What does the slope of this line tell us about the function?

Accepted Answer

The rate at which the function changes

Answer

The y-intercept of the function

Answer

The domain of the function

Answer

The range of the function

Question 34

Which equation is a linear equation?

Accepted Answer

y = 2x + 1

Answer

y = x^2 + 2

Answer

y = 3x^3 - 1

Answer

y = sin(x) + 1

Question 35

Which of the following patterns involves a sequence of numbers?

Accepted Answer

2, 4, 6, 8, 10...

Answer

Red, blue, red, blue, red...

Answer

ABC, DEF, GHI, JKL...

Answer

Monday, Wednesday, Friday, Sunday...

Question 36

Which equation represents the relationship between the number of hours worked and total pay (in dollars), if the hourly rate is $10?

Accepted Answer

y = 10x

Answer

y = x + 10

Answer

y = 10 / x

Answer

y = x / 10

Question 37

Which of the following is an example of a linear function?

Accepted Answer

y = 2x + 1

Answer

y = x^2

Answer

y = 1 / x

Answer

y = sin(x)

Question 38

What is the slope of the line represented by the equation y = -2x + 5?

Accepted Answer

-2

Answer

2

Answer

5

Answer

-5

Question 39

Which of the following is an example of an arithmetic pattern in the sequence: 1, 3, 5, 7, 9?

Accepted Answer

Adding 1 each time

Answer

Multiplying by 2 each time

Answer

Squaring each number

Question 40

What is the rule to continue this pattern: 10, 15, 20, 25, 30?

Accepted Answer

Add 5

Answer

Add 10

Answer

Add 15

Question 41

What is the next term in the geometric sequence: 2, 6, 18, 54, ...?

Accepted Answer

162

Answer

108

Answer

216

Question 42

Which of the following equations represents the relationship between the number of apples (x) and the total cost (y) if each apple costs $0.50?

Accepted Answer

y = 0.50x

Answer

y = 2x

Answer

y = 0.50 / x

Question 43

What is the slope of the line that passes through the points (2, 3) and (5, 7)?

Accepted Answer

2

Answer

1

Answer

3

Question 44

Which of the following is NOT a characteristic of a function?

Accepted Answer

The graph of the function has multiple points for each input

Answer

Each input has only one output

Answer

The relationship can be represented by a graph

Question 45

What is the domain of the function f(x) = x^2 + 2?

Accepted Answer

All numbers

Answer

Only positive numbers

Answer

Only negative numbers

Question 46

Select the graph that represents a proportional relationship:

Accepted Answer

A line passing through the origin with a consistent slope

Answer

A line not passing through the origin with a consistent slope

Answer

A parabola

Answer

A circle

Question 47

Find the inverse of the function f(x) = 2x + 3:

Accepted Answer

f^-1(x) = (x - 3)/2

Answer

f^-1(x) = 3x - 2

Answer

f^-1(x) = 2x - 3

Answer

f^-1(x) = (3x - 2)/2

Question 48

The graph shows the number of apples sold and the total cost. How many apples were sold for a total cost of $6?

Accepted Answer

3 apples

Answer

2 apples

Answer

4 apples

Answer

5 apples

Question 49

Which of the following shows a geometric pattern?

Accepted Answer

Multiplying by 3 each time

Answer

Adding 2 each time

Answer

Alternating between adding 1 and subtracting 1

Answer

Repeating the sequence 1, 2, 3 over and over

Question 50

Which of the following is a scatter plot?

Accepted Answer

A graph with dots representing data pairs

Answer

A graph with bars representing different categories

Answer

A graph with a line showing the average of data

Answer

A graph with a pie chart dividing data into sections

Question 51

The table shows the distance traveled by a car for different amounts of time. What is the relationship between the distance and the time?

Accepted Answer

Linear

Answer

Exponential

Answer

Quadratic

Answer

Logarithmic