Skip to the content
Peabody TeachFor teachers and grown-ups

Function notation and models: High school math

HS: function notation, domain/range, building functions, linear/quadratic/exponential models, trigonometric functions. A free high school lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: hS: function notation, domain/range, building functions, linear/quadratic/exponential models, trigonometric functions.

Teach (10 min)

  • 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.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/funcs.evalFx?lesson=8-funcs-evalfx-1&at=8

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. The table shows a function f. x: 1, 2, 3, 4 f(x): 4, 6, 8, 10 What is f(1)?
  • 2. The table shows a function f. x: 1, 2, 3, 4 f(x): 8, 13, 18, 23 What is f(3)?
  • 3. The table shows a function f. x: 1, 2, 3, 4 f(x): 3, 6, 9, 12 What is f(1)?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  1. The table shows a function f. x: 1, 2, 3, 4 f(x): 4, 6, 8, 10 What is f(1)?
  2. The table shows a function f. x: 1, 2, 3, 4 f(x): 8, 13, 18, 23 What is f(3)?
  3. The table shows a function f. x: 1, 2, 3, 4 f(x): 3, 6, 9, 12 What is f(1)?
  4. The table shows a function f. x: 1, 2, 3, 4 f(x): 4, 5, 6, 7 What is f(3)?
  5. The table shows a function f. x: 1, 2, 3, 4 f(x): 7, 10, 13, 16 What is f(4)?
  6. The table shows a function f. x: 1, 2, 3, 4 f(x): 6, 10, 14, 18 What is f(3)?
  7. The table shows a function f. x: 1, 2, 3, 4 f(x): 10, 15, 20, 25 What is f(4)?
  8. A function is f(x) = 2x + 4. What is f(4)?
  9. A function is f(x) = 5x + 2. What is f(−2)?
  10. The table shows a function f. x: 2, 3, 4, 5 f(x): 5, 7, 9, 11 What is f(2)?
Answers
  1. f(1) = 4
  2. f(3) = 18
  3. f(1) = 3
  4. f(3) = 6
  5. f(4) = 16
  6. f(3) = 14
  7. f(4) = 25
  8. f(4) = 12
  9. f(−2) = −8
  10. f(2) = 5

Printable sheet

Name: ____________________   Date: ____________

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)?
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

Written by Peabody from its own skill pages. Free, no ads, no sign-in. Children can practise this on Peabody. More from teachers: teacher-shared resources.