Lesson 3
Using Function Notation
These materials, when encountered before Algebra 1, Unit 4, Lesson 3 support success in that lesson.
3.1: Which One Doesn’t Belong: Function Notation (10 minutes)
Warmup
This warmup prompts students to compare four representations. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the representations for all to see. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, ask each student to share their reasoning why a particular item does not belong, and together find at least one reason each item doesn't belong.
Student Facing
Which one doesn’t belong?
 \(f(0) = 2\)
 \((0,5)\)
 \(y = x+2\)
Student Response
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Activity Synthesis
Ask each group to share one reason why a particular item does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct. During the discussion, ask students to explain the meaning of any terminology they use, such as function, input, and output. Also, press students on unsubstantiated claims.
3.2: Points into Function Notation and Back (10 minutes)
Activity
In this activity, students practice their understanding of function notation for points by converting given coordinate pairs into function notation and then writing coordinate pairs associated with values given in function notation. In the associated Algebra 1 lesson, students interpret equations like \(f(2) = 5\) in situations.
Student Facing
 A function is given by the equation \(y = f(x)\). Write each of these coordinate pairs in function notation.
 \((2,3)\)
 \((\text{}1,4)\)
 \((0,3)\)
 \((4,0)\)
 \(\left( \frac{2}{3}, \frac{3}{4} \right)\)
 A function is given by the equation \(h(x) = 5x  3\). Write the coordinate pair for the point associated with the given values in function notation.
 \(h(3)\)
 \(h(\text{}4)\)
 \(h\left( \frac{2}{5} \right)\)
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
The purpose of the discussion is to clarify the meaning of function notation and how it is connected to previous understanding of coordinate pairs. Select students to share their solutions. Ask students:
 “In the equation \(h(5) = 22\), what value is the input and what value is the output? Explain how you know.” (5 is the input and 22 is the output. This is because the input is always in the parentheses next to the function designation and it is equal to the output.)
 “A function has the output 14 when the value 99 is input. What are some ways to write this?” (in function notation like \(f(99) = 14\) or as a coordinate pair like \((99,14)\))
3.3: A Graph with Properties (20 minutes)
Student Facing

Draw a graph of function \(y = g(x)\) that has these properties:
 \(g(0) = 2\)
 \(g(1) = 3\)
 \((2,3)\) is on the graph
 \(g(5) = \text{}1\)

Han draws this graph for \(g(x)\). What is the error?
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
The purpose of the discussion is to recall the meaning of function notation and what makes a rule a function. Select students to share their responses.
Display the graph for all to see.
Ask students to discuss with a partner: “Jada draws this graph as \(g(x)\). Do you agree or disagree? Explain your reasoning.” (I agree. It has all the required points and is a function since the 4 inputs each have only 1 output. She may be thinking of a situation in which it does not make sense to have a noninteger as an input such as the number of people who are doing something.)