Function Notation

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SWBAT express the relationship between the input and output of a function with function notation.

Big Idea

Students will analyze the use of function notation when describing what is happening in a function.


10 minutes

As class begins, I will ask my students to complete today's Do Now. While students are working, I will circulate around the room passing back the graded exit cards from our last class.

After about 4 minutes, I will ask four students to come to the front of the room to walk the class through their responses to the Do-Now.  Then, we will quickly discuss the responses the students made on yesterday's Exit Card

Next a student volunteer will read today's lesson objective,  "SWBAT express the relationship between the input and output of a function using function notation".

Guided Notes + Practice

30 minutes

I will introduce function notation and reinforce the most recent concepts that we have been learning using this Presentation. I will ask to students to use their imaginations and pretend that we are planning to have a Class Carnival on our school's football field. I tell students that the goal of this Carnival is to make a lot of money, so we are going to charge our customers to sit on a ride, as well as an additional charge for the number of rotations each ride makes as they ride on it.

I will prompt students to jot down the pricing information on slide three. Then, I will ask students to create a table of values on the top of their notes with a partner. After a few minutes we will come back together and share our responses. Beneath each table, I will write down three equations that model the total cost of each ride. Here are the equations:

y = 3x + 2                        y = 2x + 1                        y = 4x + 3

I will ask students to examine the equations with a partner, and to discuss how the pricing information of each ride affected the final equation. After giving students the information on Slide 5, I will rewrite our three equations above using function notation:

f(x) = 3x + 2                        m(x) = 2x + 1                        s(x)= 4x + 3

I will ask students if they see any benefit in writing our functions using this new notation. Then, I will ask students to describe the meaning of the equations below in a complete sentence:

  • f(6) = 3(6) + 2  -> $20
    • A person rode the Ferris wheel six times and it cost $20
  • m(4) = 2(4) + 1 -> $9
    • A person rode the merry go round four times and it cost $9
  • s(7) = 4(7) + 3  -> $31
    • A person rode the swings seven times, and it cost $31

I will ask students to describe the meaning and reasonableness of m(0) and f(1.5), and to describe the domain and range of these three functions. I will also ask students to decide if this function would be continuous or discrete, and how this information would affect the graph of this function. Students will then complete the You Try the section on Slide 8.

Partner Practice

30 minutes

Students will practice working with function notation using this Function Notation Practice. I will ask students to work independently on Part 1 for 10 minutes. After 5 minutes, I will ask students to compare their paper with a neighbor to see if they are both on the right track. Next, I will ask a student volunteer to quickly review Part 1 at the front of the room.

Next, I will ask the class to spend the next 15 minutes working on Part 2 and Part 3. Students should work in pairs on these two sections. We will then review both sections as a whole group.


10 minutes

At the end of today's lesson, I will refer back to our objective and ask students to describe how function notation shows the relationship between the input and output of the function. Before leaving for the day, students will then complete an Exit Card.