Function Notation: What Does f(x) Mean?

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Mathematics · Algebra I
SP-ALG1-011 · Free to print and use in your classroom · substituteplans.com
Page 2
Function Notation: What Does f(x) Mean?
Mathematics · Algebra I · Grades 8-10 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the worked example on the board.
Technology
None. Calculators are optional for arithmetic only.
Student
independence
High. Students work alone, then compare with a partner.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard
Goal for today: Students will read and use function notation f(x) to evaluate functions for given inputs, find an input
from a given output, and interpret function values in context.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: f(x) = 3x − 2. f(4) means “replace x with 4.” f(4) = 3(4) − 2 = 10.
☐ Write this line on the board: f(4) = 10 means that when the input is 4, the output is 10.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today is about function notation. When you see f(x) = 3x − 2, think of f as a machine. You put a
number in, the machine follows the rule, and a number comes out. The notation f(4) just means “put 4 in.” It does NOT
mean f times 4. An example is on the board. Work on your own and check answers with a partner at the end.

SubstitutePlans.com
Mathematics · Algebra I
SP-ALG1-011 · Free to print and use in your classroom · substituteplans.com
Page 3
Run of show
Minutes
What you do
What students do
0–5
Take attendance the way the school requires. Hand out the
worksheet face down and ask students to wait.
Settle in and take out a pencil.
5–12
Read the board example aloud. Say: “To find f(4), replace
every x with 4 and calculate.” Then do f(−1) with students,
reminding them to put negatives in parentheses: 3(−1) − 2
= −5.
Follow along and copy the example.
12–30
Tell students to complete Part A (problems 1–8). Walk the
room. If a student is stuck, ask, “What number goes in for
x? Did you replace every x?”
Evaluate each function, showing the
substitution.
30–40
Tell students to complete the function table, Part B
(true/false 9–11), and Part C (word problems 12–13).
Partners may compare quietly.
Fill in the table, decide true or false, and
use a function in a real situation.
40–46
Read the answers from the key. Students mark each right
or wrong and fix mistakes.
Check their work and correct errors in a
different color if possible.
46–50
Have students write the exit ticket sentence, then collect
all worksheets and stack them for the teacher.
Write one sentence. Hand in the worksheet.
If things go wrong
• If students think f(4) means f × 4, point to the board: f is the name of the function, and f(4) is its output when
the input is 4.
• If a student gets a wrong answer for g(−2), remind them to put −2 in parentheses and square it: (−2)² = 4.
• If a student is stuck on problem 7, tell them f(x) = 13 means 3x − 2 = 13, and they solve it as an equation.
• If the class is noisy, remind them this is individual practice time. Partners may whisper during Part B.
Early finishers
• Write a function rule of your own, then make a table with four inputs and outputs.
• If f(x) = x + 2 and g(x) = 2x, find f(g(3)) by working from the inside out.
Support and challenge
• Support: Have students complete problems 1, 2, 3, 4 and 6, and write the substituted expression before
calculating.
• Challenge: Ask students to find f(a + 1) when f(x) = 3x − 2 and simplify the result.

SubstitutePlans.com
Mathematics · Algebra I
SP-ALG1-011 · Free to print and use in your classroom · substituteplans.com
Page 4
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: