Evaluating Functions Using Function Notation

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SWBAT evaluate a function using function notation and interpret the meaning of x and f(x) from ordered pairs and an equation.

Big Idea

The emphasis in this lesson is to make a connection from what students already know about evaluating an expression to evaluating and interpreting a function.

Warm Up

10 minutes

I intend for today's Warm Up to take about 10 minutes for the students to complete and for me to review with the class.  In this Warm Up, I am introducing the lesson by building on my students prior knowledge of evaluating expressions.  I alternate between evaluating an expression, and, evaluating the same expression using function notation.

There are three different expressions, for a total of six problems.  When reviewing the Warm Up, I introduce the idea of a coordinate pair for a function, (x, f(x)), making the connection to my students' prior understanding of evaluating expressions.  The video below provides a view on how I talk about this with my students.


Guided Practice

30 minutes

After reviewing the Warm Up, and presenting the objective for today's lesson (i.e., evaluating functions), I will hand each student a copy of the Guided Practice.  

I begin today's Guided Practice by having all students attempt the first question individually.  I am assessing their prior knowledge with respect to the use of Order of Operations. After a couple of minutes, I will ask for some student responses, writing all of the responses on the board.

The correct answer is 32. It is usually the case that several of my students will respond with 18. This result is easy to get if a student fails to evaluate eight divided by two before finding the sum. My students generally know this, but I find it is helpful to begin this section of the lesson with a problem that reminds them of the Order of Operations used when evaluating expressions or equations. 

With the importance of order of operations on their minds, I next have my students complete each section of the lesson. We'll have a check-in at the end of each section to allow for discussion and questions.  I will randomly call on students as we review each section.  The sections covering the following learning objectives:

  • Evaluating functions using f(x)
  • Understanding the use of different variables for different functions
  • Knowing how to simplify given functions with different math operations
  • Recognizing f(x)= y as an ordered pair
  • Plotting points from the ordered pair
  • Stating the range f(x) from given domain values of x
  • Using the ordered pairs in the form f(x)=y to write the equation of a line          

The final application topic, writing the equation of a line from two points using function notation, presents a significant challenge for my students.  Students have previously wrote the equation of a line from two points, but I expect many will need help remembering the process. I find that by the end of the lesson, many are able to correctly identify the ordered pairs using function notation, but they struggle with the calculation of slope. Given this, I have planned to assess the students on this skill using the Exit Slip at the end of the lesson.

Independent Practice

20 minutes

Today's Independent Practice focuses more attention on correctly evaluating functions. I want my students to be able to evaluate functions on their own by the end of today's lesson. In my course, understanding the meaning of the representation (x, f(x)) is necessary for students to be able to interpret functions meaningfully. 

Some of the practice problems provide students with a given value for x, and students need to evaluate f(x). Problems four to eight provide students with the output from the function f(x), asking students to solve for x. I expect my students will have more difficulty solving equations for x, then evaluating the function when given x.  

With about ten minutes left in class, I will assign the remainder of the Independent Practice as homework if students have not completed the handout.  Then, I will distribute the Exit Slip for students to complete before they leave. 

Exit Slip

10 minutes

Today's Exit Slip is a quick assessment of student understanding.  The Exit Slip contains problems to check for student understanding of (x, f(x)) as a notation, and their ability to apply it to calculate rate of change.  

Problem 1 assesses each students ability to recognize the ordered pairs given in the form f(x)=y and write the equation of the line.  I have students work one this Exit Slip quietly, so that I can get an indication of each student's understanding of this application.

In the second problem, are asked to use a function to model a real world scenario. In the problem x represents the number of days. f(x) represents the number of people (in thousands) who are sick with flu virus.  The responses should have been similar to the ones given below.

a) f(6)= 3(6) = 13   (13,000 people got the flu in six days)

b) How many people did the flu spread to in two days?

c)  If the flu spread to 16,000 people, how many days did it take?

d)  Students needed to plot two sets of ordered pairs or points that made the equation f(t)=3t- 5 true.

Before my students leave for the day, I hope that we will discuss whether or not we need a restriction on the domain of this function.