Function Tables

There some special equations that have a formal name called a function. Functions are written in many different forms, but we will concern ourselves mainly with these. 3y x

2y x 2 8y x 2 5y x

Notice that all of these equations have an ‘x’ and a ‘y’. Later on the ‘y’ will be replaced with ‘f(x)’, which we say as ‘f’ of ‘x’. So, ‘y’ and ‘f(x) represent the same thing.

There are times where you will need to match the function (equation) to a table or a table to a function (equation). When we do this the table is know as a function table.

Example: Does the function y = x + 3 represent the data in the table?

y ( f(x) ) x

5 2

10 7

12 9

What do you think we should do to answer the question?

We need to substitute the values in our table into the function (equation).

y ( f(x) ) x

5 2

10 7

12 9

3y x

5 2 3

5 5

3y x

10 7 3

10 10

3y x

12 9 3

12 12

Since we have 3 rows with values we will need to solve the function 3 times. We call this Plug and Chug.

We can also be given a function table and we have to find the correct function rule.

x y [f(x)]

4 2

5 3

6 4

A. y = x - 5

B. y = x + 1

C. y = x - 2

D. y = x - 1

In this case we will need to plug our values in to A, B, C, and D.

A. y = x - 5 B. y = x + 1 C. y = x - 2 D. y = x - 1

2 = 4 - 52 = -1

2 = 4 + 1

2 = 5

2 = 4 - 1

2 = 3

2 = 4 - 2

2 = 2

C. y = x - 2

3 = 5 - 2

3 = 3

C. y = x - 2

4 = 6 - 2

4 = 4

x y [f(x)]

4 2

5 3

6 4

A. y = x - 5

B. y = x + 1

C. y = x - 2

D. y = x - 1

Notice we worked out the problem until we prove it either works for every value in our table or we prove it did not work for the values in our table.

We can also be given the function and have to find the correct function table.Which of the following tables represents the function y = 2x + 8.

x y [f(x)]

4 2

5 3

6 4

x y [f(x)]

1 10

3 14

5 18

x y [f(x)]

3 12

5 31

6 45

x y [f(x)]

1 3

2 6

3 8

A C

B D

A. y = 2x + 8 B. y = 2x + 8 C. y = 2x + 8 D. y = 2x + 8

2 = 2(4) + 8

2 = 16

10 = 2(1) + 8

10 = 10

3 = 2(1) + 8

3 = 10

12 = 2(3) + 8

12 = 14

2 = 8 + 8 10 = 2 + 8

B. y = 2x + 8

14 = 2(4) + 8

14 = 14

14 = 6 + 8

B. y = 2x + 8

18 = 2(5) + 8

18 = 18

18 = 10 + 8

12 = 6 + 8 3 = 2 + 8

Which of the following tables represents the function y = 2x + 8.

x y [f(x)]

4 2

5 3

6 4

x y [f(x)]

1 10

3 14

5 18

x y [f(x)]

3 12

5 31

6 45

x y [f(x)]

1 3

2 6

3 8

A C

B D

There are no short cuts to these types of problems. You have to do all the math for every single function and function table.