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🧩 High school math · Patterns & Algebra

Function notation and models

f(4) means the output of f when the input is 4. Put 4 where x is. If f(x) = 3x − 5, then f(4) = 3 × 4 − 5 = 7. In a table, read the output below the input.

Worked example

The table shows a function f.
x: 1, 2, 3, 4
f(x): 5, 6, 7, 8
What is f(1)?
Answer: f(1) = 5
Find x = 1 in the table and read the f(x) below it: 5.

For grown-ups: HS: function notation, domain/range, building functions, linear/quadratic/exponential models, trigonometric functions. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS F-IF
  • CCSS F-BF
  • CCSS F-LE
  • CCSS F-TF
What this practises, for teachers

Practices hS: function notation, domain/range, building functions, linear/quadratic/exponential models, trigonometric functions (F-IF, F-BF, F-LE, F-TF). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. The table shows a function f.
    x: 1, 2, 3, 4
    f(x): 4, 6, 8, 10
    What is f(1)?
    Show the answer and how
    Answer: f(1) = 4
    Find x = 1 in the table and read the f(x) below it: 4.
  2. The graph shows a function f. What is f(3)?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456
    Show the answer and how
    Answer: f(3) = 5
    Go to x = 3 on the graph and read how high the line is there: 5.
  3. A function is f(x) = x − 12. What is f(−5)?
    Show the answer and how
    Answer: f(−5) = −17
    f(−5) means put −5 in place of x: 1 × −5 − 12 = −17.

Before and after

Learn first: Graphs that tell stories (8th)

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Function notation and models (High school)

  1. A function is f(x) = 4x + 9. What is f(4)?
  2. A function is f(x) = x + 9. What is f(4)?
  3. The table shows a function f.
    x: 1, 2, 3, 4
    f(x): 3, 5, 7, 9
    What is f(4)?
  4. A function is f(x) = 4x + 7. What is f(2)?
  5. The table shows a function f.
    x: 1, 2, 3, 4
    f(x): 11, 16, 21, 26
    What is f(2)?
  6. The graph shows a function f. What is f(3)?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456
  7. A function is f(x) = −3x + 7. What is f(0)?
  8. The table shows a function f.
    x: 1, 2, 3, 4
    f(x): 5, 9, 13, 17
    What is f(2)?
  9. The table shows a function f.
    x: 2, 3, 4, 5
    f(x): 14, 17, 20, 23
    What is f(2)?
  10. The graph shows a function f. What is f(−2)?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456
  11. A function is f(x) = 2x + 12. What is f(1)?
  12. A function is f(x) = x + 9. What is f(6)?

Answer key

  1. f(4) = 25
  2. f(4) = 13
  3. f(4) = 9
  4. f(2) = 15
  5. f(2) = 16
  6. f(3) = −3
  7. f(0) = 7
  8. f(2) = 9
  9. f(2) = 14
  10. f(−2) = 1
  11. f(1) = 14
  12. f(6) = 15

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