Same Math › Algebra 1 · grades 8–10 › Function tables and function machines
What is a function table?
A function is a rule that turns each input into exactly one output. Classes draw it as a machine: 3 goes in, the rule “× 2, then + 1” runs, and 7 comes out. A function table lists inputs (x) and outputs (y) side by side, and kids either fill in the outputs or work backwards to find the rule.
- Input (x): what goes into the machine.
- Output (y): what comes out.
- A function gives each input exactly one output.
Why schools teach it
It's the idea every graph is built on
Eighth grade and Algebra 1 define a function as a rule assigning each input exactly one output (8.F.A.1 and HSF.IF.A.1). Tables, equations and graphs are three views of the same rule.
Finding the rule from a table is how kids learn to read slope: if y goes up by 2 every time x goes up by 1, the rule starts with 2x.
At the kitchen table
What to say, and what to skip
Say this
What's the rule? Say it in words first.
“Double it, then add 1.”How much does y change each time x goes up by 1?
That's the number in front of x.What is y when x is 0?
That's the number added at the end.Does any input have two different outputs?
Then it's not a function.
Skip this
- Guessing the rule from the first row only.Check it on every row.
- Thinking repeated outputs break a function.Two inputs can share an output. One input can't have two.
- Mixing up x and y columns.x goes in; y comes out.
See it in action
Finding the rule for x: 0, 1, 2, 3 and y: 4, 7, 10, 13
How much does y go up each step?
3 each timeSo the rule starts with 3x. What's y at x = 0?
4Write the rule and check a row
y = 3x + 4; at x = 2, 6 + 4 = 10 ✓
If x jumps by 2 instead of 1, divide the change in y by 2.
Free practice sheet
Make a function table sheet
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Parents also ask
Is a function table the same as an in-out box?
Yes. Elementary classes call it an in-out box; Algebra 1 calls it a function table.
What makes something not a function?
One input with two different outputs, like x = 2 giving both 5 and 7.
What if the x values skip, like 0, 2, 4?
Divide the change in y by the change in x to get the number in front of x.
Do all function tables make lines?
No. A constant change makes a line. Doubling makes an exponential curve, and squaring makes a parabola.