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Understanding Functions Practice

Practice Problem #1

Given the relation {(−5, 3), (4, 7), (−2, −3), (6, 7)}, determine the domain, range, and whether the relation is a function.

What is the domain of the relation?

  1. −3, 3, 7
  2. −5, −2, 4, 6
  3. −5, 3, 4, 7, −2, −3, 6, 7

Answer: b. −5, −2, 4, 6. The domain is the first number in each pair listed in order from least to greatest.

What is the range of the relation?

  1. −3, 3, 7
  2. −5, −2, 4, 6
  3. −5, 3, 4, 7, −2, −3, 6, 7

Answer: a. −3, 3, 7. The range is the second number in each pair of numbers, also listed in order from least to greatest. Remember to not write repeated values.

Is this relation a function?

  1. Yes
  2. No

Answer: a. Yes. This relation is a function because each x-value (domain value) corresponds to one and ony one y-value (range value).

Practice Problem #2

Given the relation {(0, −1), (−5, 4), (−1, 6), (0, 12), (1, −1)}, determine the domain, range, and whether the relation is a function.

What is the domain of the relation?

  1. −1, 1, 4, 0, 12
  2. −1, 0, 4, 6, 12
  3. −5, −1, 0, 1

Answer: c. −5, −1, 0, 1. The domain is the first number in each pair of coordinates, also called x-values. Write numbers in order from least to greatest and do not repeat any numbers.

What is the range of the relation?

  1. −1, 1, 4, 0, 12
  2. −1, 4, 6, 12
  3. −5, −1, 0, 1

Answer: b. −1, 4, 6, 12. The range of the function is the second value in each pair of numbers. Remember to not write repeated values and write your values in order from least to greatest.

Is this relation a function?

  1. Yes
  2. No

Answer: b. No. The correct answer is no because you have repeated x-values (or domain values). For the relation to be a function, you cannot have an x-value that corresponds to more than one y-value.

Practice Problem #3

Determine if the mapping is a function.

mapping with an x column of the numbers negative 1, 5, 7, and 12 and a y column of the numbers 4, negative 3, and 9. A circle is drawn around the x column and a circle is drawn around the y column. An arrow from negative 1 in the x column points to 4 in the y column. An arrow from 5 in the x column points to negative 3 in the y column. An arrow from 7 in the x column points to 9 in the y column. An arrow from 12 in the x column points to 4 at the top of the y column

Is this mapping a function?

  1. Yes
  2. No

Answer: a. Yes. This is a function because none of the domains are used more than once.

Practice Problem #4

Given the relation below, draw a mapping to represent the relation. Then determine if it represents a function.

Relation: (−2, 5), (0, 3.5), (2, 5), (5, 0)

Domain

  • −2
  • 0
  • 2
  • 5

Range

  • 0
  • 3.5
  • 5

Map the relation.

Answer:

mapped relation with two columns: one Domain column and one Range column. The negative 2 in the domain column is mapped to the 5 in the range column. The 0 in the domain column is mapped to the 3.5 in the range column. The 2 in the domain column is mapped to the 5 in the range column. The 5 in the domain column is mapped to the 0 in the range column.

Is this a function?

  1. Yes
  2. No

Answer: a. Yes. This is a function, as none of the domains are used more than once.

Practice Problem #5

Given the relation below, draw a mapping to represent the relation. Then determine if it represents a function.

Relation: (−4, 2.1), (3, 10), (0, 2.1), (−4, 5)

Domain

  • −4
  • 0
  • 3

Range

  • 2.1
  • 5
  • 10

Map the relation.

Answer:

mapped relation with two columns: one Domain column and one Range column. The negative 4 in the domain column is mapped to the 2.1 in the range column and to the 5 in the range column. The 0 in the domain column is mapped to the 2.1 in the range column. The 3 in the domain column is mapped to the 10 in the range column.

Is this a function?

  1. Yes
  2. No

Answer: b. No. This is not a function, as one of the domains (−4) is used more than once.

Practice Problem #6

Use the vertical line test to determine whether or not the following relation is a function.

Relation: (4, 2), (4, −2), (0, 0), (1, 1), (1, −1)

Graph of a parabola starting at the origin (0,0) opening to the right and passing through the plotted points (1,1), (1, negative 1), (4,2), and (4, negative 2)
See larger version of graph.

Is this a function?

  1. Yes
  2. No

Answer: b. No. This is not a function. The vertical line crosses the relation in more than one location.

Practice Problem #7

Determine if the graph is a function.

V-shaped absolute value function graph
See larger version of graph.

Is this graph a function?

  1. Yes
  2. No

Answer: a. Yes. The graph is considered a function because it passes the vertical line test.

Practice Problem #8

Determine if the graph is a function.

graph of a line with multiple curves that looks like a sideways S-curve
See larger version of graph.

Is this graph a function?

  1. Yes
  2. No

Answer: b. No. The graph is not a function because it fails the vertical line test.

Practice Problem #9

Determine if the graph is a function.

graph of a straight, diagonal line
See larger version of graph.

Is this graph a function?

  1. Yes
  2. No

Answer: a. Yes. The graph is considered a function because it passes the vertical line test.

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