Function Tables and Graphs Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Function Tables and Graphs.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A function table (input-output table) lists paired values of a function, and its graph is the visual representation of those pairs as points on the coordinate plane.

A function is like a machine: put a number in, get a number out. The table records what goes in and comes out, and the graph draws the picture.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Tables, graphs, equations, and words can represent the same function.

Common stuck point: The procedure for function tables and graphs is the easy part; the trap is plotting $(y,x)$ instead of $(x,y)$ . Asking "Can I match each table row to a graph point?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Can I match each table row to a graph point?

Worked Examples

Example 1

medium

Table:

x:0,1,2,3

y:3,6,11,18

. Is it linear? Justify by looking at first and second differences.

Answer

No, quadratic (

y = x^2 + 2x + 3

)

First step

First differences:

3,5,7

— not constant.

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Example 2

medium

A table records a runner's distance:

t

(min):

0,1,2,3

;

d

(mi):

0,0.2,0.4,0.6

. Write a rule and predict distance at

t=10

Example 3

hard

Two graphs

y=2x+1

and

y=-x+7

. Find their intersection.

Example 4

hard

Build a table for

y=|x|

x=-2,-1,0,1,2

and describe the graph.

Example 5

challenge

y

varies linearly with

x

y=2

when

x=1

and

y=8

when

x=4

. Find

y

when

x=10

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A table shows

x:1,2,3

and

y:3,6,9

. What is

y

when

x=4

Example 2

easy

For

y = x + 5

, complete the pair when

x = 2

Example 3

easy

In a table, which column is usually the input?

Example 4

easy

A graph passes through

(0, 2)

. What is the

y

-intercept?

Example 5

easy

A table has

x:0,1,2

y:0,1,4

. Is

y=x

the rule?

Example 6

easy

The graph of

y=2x

— does it pass through the origin?

Example 7

easy

From

x:1,2,3,4

and

y:5,5,5,5

, what kind of function is it?

Example 8

easy

A graph is a straight line. What family of function is it?

Example 9

medium

A table shows

x:1,2,3

y:4,7,10

. Find the rule.

Example 10

medium

Graph of

y = x^2

: is it a straight line or a curve?

Example 11

medium

From the table

x:0,1,2,3

y:1,2,4,8

, find

y

x=4

Example 12

medium

A line on a graph rises 2 for every 1 right and hits

(0,1)

. Write its equation.

Example 13

medium

A table is

x:2,4,6

y:1,2,3

. Express

y

in terms of

x

Example 14

medium

Which input gives output 0 for

y = 2x - 6

(use a table idea)?

Example 15

medium

A graph shows points

(1,2),(2,4),(3,6)

. Are they on one line through the origin?

Example 16

medium

A table of perimeter

P

vs side

s

for a square:

s:1,2,3

P:4,8,12

. Find the rule.

Example 17

challenge

A table

x:1,2,3,4

gives

y:2,5,10,17

. Find a rule.

Example 18

challenge

Two graphs:

y=2x

and

y=x+3

. At what point do they meet?

Example 19

challenge

A graph of

y=f(x)

passes the vertical line test. What does that guarantee?

Example 20

medium

A table shows

x:0,1,2

and

y:5,8,11

. What is the

y

-intercept of its graph?

Example 21

easy

For

y = x - 3

, find

y

when

x = 8

Example 22

easy

A table has

x:0,1,2,3

and

y:0,2,4,6

. Write the function rule.

Example 23

easy

Which is the correct point to plot from the table row

x=2,\ y=7

Example 24

easy

From

y = 4x

, complete the row for

x = 5

Example 25

easy

Which graph passes through the origin? (A)

y=x+2

(B)

y=3x

(C)

y=x-1

Example 26

medium

A table

x:1,2,3,4

and

y:5,9,13,17

. Find the rule.

Example 27

medium

Cost

C

to print

n

tickets:

C = 3n + 5

. What does the 5 represent?

Example 28

medium

A line on a graph passes through

(0,-2)

and

(3,4)

. Find its equation.

Example 29

medium

A table for

f

x:1,2,3

f(x):2,4,8

. Predict

f(4)

assuming the pattern continues.

Example 30

medium

Find the

x

-intercept of

y = 3x - 12

Example 31

medium

\{(1,2),(2,5),(1,7)\}

a function?

Example 32

medium

Two tables: A has

y=3x

; B has

y=x+6

. Which input makes them agree?

Example 33

medium

Graph passes through

(2,3)

with slope

-1

. Find its equation.

Example 34

hard

Population

P

doubles each year:

P_0 = 50

. Make the rule and find

P_3

Example 35

hard

From the table

x:0,1,2,3,4

and

y:0,1,4,9,16

, find

y

x=10

Example 36

hard

f(x)=2x+1

and

g(x)=3x-4

. For what

x

does

f(x)=g(x)

Example 37

hard

A table represents a discrete function: pages read per day. Why might it NOT make sense to connect the dots on its graph?

Example 38

hard

A table shows

x:1,2,3,4

and

y:12,6,4,3

. Find the rule.

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Related Concepts

Ordered Pairs Function as Mapping Coordinate Plane Linear Functions Quadratic Functions

Background Knowledge

These ideas may be useful before you work through the harder examples.

ordered pairsfunction as mappingcoordinate plane