Evaluating Functions Day 2

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Objective

SWBAT evaluate a function from an equation and a graph. SWBAT determine the domain and range of a function.

Big Idea

Students who understand functions well can make connections between the graph of a function and the equation of the function.

Open

10 minutes

Students should work with their partner on each slide of the evaluating_functions_2_opening activity.  On the first slide, students are using a graph to evaluate a function for two given input values.  As students are working, move around the room to monitor student progress.  The evaluation of f(-1) should be fairly straight forward for students.  This question will give you a sense of whether or not students understand the basics of evaluating functions.  Evaluating f(2) will require students to make sense of both the graph and the open and closed circles (MP1)(MP2).

When you bring the class together to share out use a non_verbal to see how each pair of students is thinking (students can hold up a certain number of fingers to show the output value).   Challenge students to explain their solution to question #2.  Also, don't tell students whether or not they are correct at first.  Let students argue their ideas with other members of the class (MP3).

In the second slide students should determine the domain of the same piecewise function.  Students will need to address whether or not the "jump" in the graph affects the domain.  Let students discuss this with a partner first and then open up a whole class discussion.  Help guide the discussion back to the domain being all of the input values for the function.  Since all of the x-values between -6 and 7 (including 2) yield an output value the domain of function f is [-6,7].

Independent Practice

20 minutes

Students should work with partners on evaluate_functions_2_practice.  This worksheet provides students some time to practice and apply what they have been learning in previous classes.

As students are working, there are some things that you will want to watch out for as a teacher:

1) In Question #1f and Question #1h watch for students who are writing 31 and 2 respectively for their solutions.  This is a common mistakes that students will make.  Rather than solving for x, they are substituting the f(x) value for x in the equation.  

2) In Question #2e, ensure that students have 3 solutions.  The question is saying to find the x values where the function has an output of 2.  There are three places on the graph where this happens (MP2).

3) In question #3, students will often write that the range is [-4,1].  Make sure that they realize that the range is a list of all possible output values.

4) In question #4, students will make the connection between evaluating a function and the graph that a function represents (MP4).  Ensure that when students are squaring their negative values they are doing so correctly.

5) Ensure that students are correctly graphing the output values at x=4.  

Closure

10 minutes

Give students sufficient time to work on the functions_representations exit ticket.  Now that students have had some time to practice with a classmate, you can evaluate their understanding of the concepts.  Questions 1-3 test students mastery of the concepts and skills worked on during the independent practice.  Question #4 requires students to identify the domain for a square root function (MP1 and MP2) and explain their reasoning (MP3).