Same Math › Algebra 1 · grades 8–10 › Function notation
What does f(x) mean?
f(x) is read “f of x,” and it's just a name for the output. If f(x) = 2x + 1, then f(3) means “put 3 in for x”: 2(3) + 1 = 7. It does not mean f times 3. Kids also work backwards: if f(x) = 11, which x gives 11? Solve 2x + 1 = 11, so x = 5.
- f(3): the output when the input is 3.
- f(x) = 11: find the input that gives 11.
- The parentheses don't mean multiply.
Why schools teach it
It names the input and the output together
Algebra 1 students use function notation and evaluate functions for inputs in their domain (HSF.IF.A.2). Writing f(3) = 7 says the input and the output in one line, which y = 7 can't.
It also lets a class talk about several functions at once, like f(x) and g(x), which matters in Algebra 2.
At the kitchen table
What to say, and what to skip
Say this
What goes in for x?
Can you rewrite it with the number in parentheses?
2(3) + 1 instead of 23 + 1.Are you finding the output or the input?
f(4) = ? or f(x) = 4?Can you check it by plugging back in?
Skip this
f(3) means f times 3.
It means the output when x is 3.- Plugging in without parentheses.With x = −2, x² is (−2)² = 4, not −4.
- Mixing up f(x) = 5 and f(5).One gives you the output; the other gives you the output to work backwards from.
See it in action
Using f(x) = x² − 3x
Find f(4)
4² − 3(4) = 16 − 12 = 4Find f(−2)
(−2)² − 3(−2) = 4 + 6 = 10So
f(4) = 4 and f(−2) = 10
Put the number in parentheses every time, especially negatives.
Free practice sheet
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Parents also ask
Why not just write y?
f(3) = 7 tells you the input and the output at once. With several functions, f and g keep them apart.
Can the letter be something other than f?
Yes: g(x), h(t), C(n). The letter just names the function.
What is f(x + 1)?
Replace x with x + 1 everywhere. That's Algebra 2 work; Algebra 1 mostly uses numbers.
What does f(x) = 0 mean?
Find the inputs that make the output zero: the x-intercepts.