2.12 (Function Families: Multiple Representations)

2.12 (Function Families: Multiple Representations)

Aim: How can I identify & explain which function family multiple representations belong to?

Poll

Do Now: Which key feature is most important to YOU in determining which function family best models any given situation?

Be prepared to explain why.

• Finding the type of rate of change on a table

• Looking at the shape of the graph

• Knowing the general equation structure

• Analyzing key words to determine the type of rate of change.

Mini-Lesson

We can annotate any representation to reveal the type of function family that best models the situation.

The strategies for annotating multiple representations:

• Words/Context: Look for Key words/phrases that reveal the rate of change or maximum/minimum points

• Table: Annotate for the rate of change

• Graph: Look for the shape of the graph

• Equations: Look at the structure of equation

• Ask yourself questions: Does it have x(input) as the exponent? Is the highest degree(exponent) equal to 2? Does it the absolute value bars? Does it only have a coefficient or constant?

Open Ended

Annotate at least one of the representations to determine which function family (linear, absolute value, exponential, or quadratic) best models the given situation.

Explain how you know.

Multiple Select

Each representation shown, is a model of an Absolute Value function.

Select which statement(s) accurately justify why the representations belong to the Absolute Value function family.

• A key feature of an absolute value function is the graph will have a 'V' shape with a vertex (max/min point).

• A key feature of an absolute value function is the structure of the equation will have the absolute value bars.

• A key feature of an absolute value function is when annotating the table, there will be two constant rates of change (one positive & one negative) changing at the vertex.

• A key feature of an absolute value function are words like doubling (x2), halving (x1/2), or tripling (x3)

Multiple Select

Which representation(s) below, belong to the Exponential function family? Select at least one.

Be prepared to discuss how you know.

•  $f\left(x\right)=\left|x+3\right|$  

Poll

Use the emoji chart to rate how confident are you in identifying Function Families in multiple representations?

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What to do next?

Based on your response to the reflection survey, and how today's lesson went for you today do the following:

1. Need more practice & further explanation --> Go to Khan Academy

2. Have a good understanding and ready to out your learning to the test --> Go to DeltaMath

3. At home, share what you learned about the different types of function families and find a real world function in your home, job (yours or your guardians), favorite show, where ever! & share what you found with the class tomorrow!