M
Math Coach Amy
Amy Ferguson Moncure

Algebra 1 · Unit 2

Is it a Function

Decide whether a relation is a function from points, a table, a map, or a graph.

Jump to section:

Key Ideas Easy 1 · Points Easy 2 · Table Easy 3 · Maps Easy 4 · Graphs
What to Remember

Points, tables, and maps

Every x value has EXACTLY one y value.

A repeated y-value is allowed. Two pairs can share a y-value.

If the same pair is listed twice, it is still one pair.

If one x-value is paired with two different y-values, it is not a function.

Graphs

Vertical line test: a vertical line must hit the graph at most once.

If any vertical line hits the graph more than once, it is not a function.

A vertical line graph fails the test. A horizontal line passes.

Easy 1

Points

Every x value has EXACTLY one y value.

Example
Is this a function? {(−2, 5), (0, 1), (3, 5), (4, −2)}

Every x value has EXACTLY one y value.

Each ordered pair is (x, y).

x = −2 is paired with y = 5.

x = 0 is paired with y = 1.

x = 3 is paired with y = 5.

x = 4 is paired with y = −2.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

1
Is this a function? {(1, 4), (2, −3), (5, 0), (2, 6)}
Show Answer

Every x value has EXACTLY one y value.

Each ordered pair is (x, y).

x = 1 is paired with y = 4.

x = 2 is paired with y = −3 and y = 6.

x = 5 is paired with y = 0.

x = 2 does not fit that rule.

No. It is not a function.

Answer: No

2
Is this a function? {(−4, −1), (−1, 2), (0, 2), (3, 7)}
Show Answer

Every x value has EXACTLY one y value.

Each ordered pair is (x, y).

x = −4 is paired with y = −1.

x = −1 is paired with y = 2.

x = 0 is paired with y = 2.

x = 3 is paired with y = 7.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

3
Is this a function? {(−5, 3), (1, 3), (1, 3), (4, 0)}
Show Answer

Every x value has EXACTLY one y value.

Each ordered pair is (x, y).

x = −5 is paired with y = 3.

x = 1 is paired with y = 3.

x = 4 is paired with y = 0.

(1, 3) is listed more than once. It is still one pair.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

4
Is this a function? {(0, −2), (0, 4), (3, 1)}
Show Answer

Every x value has EXACTLY one y value.

Each ordered pair is (x, y).

x = 0 is paired with y = −2 and y = 4.

x = 3 is paired with y = 1.

x = 0 does not fit that rule.

No. It is not a function.

Answer: No

5
Is this a function? {(−3, −3), (1, 0), (2, 5), (6, −1)}
Show Answer

Every x value has EXACTLY one y value.

Each ordered pair is (x, y).

x = −3 is paired with y = −3.

x = 1 is paired with y = 0.

x = 2 is paired with y = 5.

x = 6 is paired with y = −1.

Yes. It is a function.

Answer: Yes

Easy 2

Table

Every x value has EXACTLY one y value.

Example
Is this a function?
x−2011
y3524

Every x value has EXACTLY one y value.

Each column is one pair (x, y).

x = −2 is paired with y = 3.

x = 0 is paired with y = 5.

x = 1 is paired with y = 2 and y = 4.

x = 1 does not fit that rule.

No. It is not a function.

Answer: No

1
Is this a function?
x0123
y4444
Show Answer

Every x value has EXACTLY one y value.

Each column is one pair (x, y).

x = 0 is paired with y = 4.

x = 1 is paired with y = 4.

x = 2 is paired with y = 4.

x = 3 is paired with y = 4.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

2
Is this a function?
x−3−124
y05−21
Show Answer

Every x value has EXACTLY one y value.

Each column is one pair (x, y).

x = −3 is paired with y = 0.

x = −1 is paired with y = 5.

x = 2 is paired with y = −2.

x = 4 is paired with y = 1.

Yes. It is a function.

Answer: Yes

3
Is this a function?
x1353
y26−18
Show Answer

Every x value has EXACTLY one y value.

Each column is one pair (x, y).

x = 1 is paired with y = 2.

x = 3 is paired with y = 6 and y = 8.

x = 5 is paired with y = −1.

x = 3 does not fit that rule.

No. It is not a function.

Answer: No

4
Is this a function?
x−4−202
y73−13
Show Answer

Every x value has EXACTLY one y value.

Each column is one pair (x, y).

x = −4 is paired with y = 7.

x = −2 is paired with y = 3.

x = 0 is paired with y = −1.

x = 2 is paired with y = 3.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

5
Is this a function?
x2258
y−1406
Show Answer

Every x value has EXACTLY one y value.

Each column is one pair (x, y).

x = 2 is paired with y = −1 and y = 4.

x = 5 is paired with y = 0.

x = 8 is paired with y = 6.

x = 2 does not fit that rule.

No. It is not a function.

Answer: No

Easy 3

Maps

Every x value has EXACTLY one y value.

Example
Is this a function?
xy32174

Every x value has EXACTLY one y value.

Each arrow pairs an x-value with a y-value.

x = 1 is paired with y = 4.

x = 2 is paired with y = 4.

x = 3 is paired with y = 7.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

1
Is this a function?
xy30521
Show Answer

Every x value has EXACTLY one y value.

Each arrow pairs an x-value with a y-value.

x = 0 is paired with y = 2 and y = 5.

x = 3 is paired with y = 1.

x = 0 does not fit that rule.

No. It is not a function.

Answer: No

2
Is this a function?
xy41−230−1
Show Answer

Every x value has EXACTLY one y value.

Each arrow pairs an x-value with a y-value.

x = −2 is paired with y = 0.

x = 1 is paired with y = 3.

x = 4 is paired with y = −1.

Yes. It is a function.

Answer: Yes

3
Is this a function?
xy2−1−32
Show Answer

Every x value has EXACTLY one y value.

Each arrow pairs an x-value with a y-value.

x = −3 is paired with y = 2.

x = −1 is paired with y = 2.

x = 2 is paired with y = 2.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

4
Is this a function?
xy4130−2
Show Answer

Every x value has EXACTLY one y value.

Each arrow pairs an x-value with a y-value.

x = 1 is paired with y = −2.

x = 4 is paired with y = 0 and y = 3.

x = 4 does not fit that rule.

No. It is not a function.

Answer: No

5
Is this a function?
xy30−1−451−3
Show Answer

Every x value has EXACTLY one y value.

Each arrow pairs an x-value with a y-value.

x = −4 is paired with y = 1.

x = −1 is paired with y = 5.

x = 0 is paired with y = −3.

x = 3 is paired with y = 5.

A repeated y-value is allowed.

Yes. It is a function.

Answer: Yes

Easy 4

Graphs

Use the vertical line test.

Example
Is this a function?
−5−4−3−2−112345−5−4−3−2−112345xy

Vertical line test: a vertical line must hit the graph at most once.

Draw a vertical line at x = 0.

It hits (0, 2) and (0, −2).

It does not pass the vertical line test.

No. It is not a function.

−5−4−3−2−112345−5−4−3−2−112345xy

Answer: No

1
Is this a function?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Vertical line test: a vertical line must hit the graph at most once.

Draw a vertical line at x = 0.

It hits (0, 1) once.

No vertical line hits more than once.

Yes. It is a function.

−5−4−3−2−112345−5−4−3−2−112345xy

Answer: Yes

2
Is this a function?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Vertical line test: a vertical line must hit the graph at most once.

Draw a vertical line at x = −3.

The vertical line lies on the graph, so it hits more than once.

It does not pass the vertical line test.

No. It is not a function.

−5−4−3−2−112345−5−4−3−2−112345xy

Answer: No

3
Is this a function?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Vertical line test: a vertical line must hit the graph at most once.

Draw a vertical line at x = 2.

It hits (2, 2) once.

No vertical line hits more than once.

Yes. It is a function.

−5−4−3−2−112345−5−4−3−2−112345xy

Answer: Yes

4
Is this a function?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Vertical line test: a vertical line must hit the graph at most once.

Draw a vertical line at x = 2.

It hits (2, 3) and (2, −1).

It does not pass the vertical line test.

No. It is not a function.

−5−4−3−2−112345−5−4−3−2−112345xy

Answer: No

5
Is this a function?
−5−4−3−2−112345−5−4−3−2−112345xy
Show Answer

Vertical line test: a vertical line must hit the graph at most once.

Draw a vertical line at x = 0.

It hits (0, −2) once.

No vertical line hits more than once.

Yes. It is a function.

−5−4−3−2−112345−5−4−3−2−112345xy

Answer: Yes

Need help deciding whether it is a function?

Book a Session with Amy