Lesson 5 Give Me Five Practice Understanding

Learning Focus

Interpret function notation to match a function with its features.

How can I visualize a graph from knowing its features?

How can function notation describe a function?

How does function notation describe relationships between two functions?

Technology guidance for today’s lesson:

Add Two Functions Together Graphically: Casio ClassPad Casio fx-9750GIII

Open Up the Math: Launch, Explore, Discuss

1.

You have two sets of cards, A cards and B cards.

Lay out all the A cards. Each A card gives you a representation of a function.
Select a B card and read each statement aloud.
Find an A card that matches all 5 statements on the B card and justify each statement.
Record the match and your justification for it.
Keep the pairs together for the next part of the lesson.

Proceed until all the A and B cards are matched. Be sure that you can justify all 5 statements on the B card with the function that you match it with.

A card	B card	Reason
A1 matches with:
A2 matches with:
A3 matches with:
A4 matches with:
A5 matches with:
A6 matches with:

After you match the cards, complete the information below. Use both the A and the B cards in the pair for reference:

2.

Complete this information about the pair of cards that includes A1

Write the equation of $f (x)$ and use it to:

Find an exact value for $f (3)$ :

Find where $f (x) = - 1$ :

3.

Complete this information about the pair of cards that includes A2

What are the intervals of increase and decrease for $f (x)$ ?

Increasing:

Decreasing:

4.

Complete this information about the pair of cards that includes A3

Graph $f (x) + g (x)$ from $[- 1, 3]$ :

5.

Complete this information about the pair of cards that includes A4

Write the equation and graph $f (x)$ :

Equation:

6.

Complete this information about the pair of cards that includes A5

Which function is changing faster in the interval $[- 5, 1]$ ? Why?

7.

Complete this information about the pair of cards that includes A6

Write the equation for $g (x) + f (x)$ :

Find $g (3) + f (3)$ :

Ready for More?

1.

Explain the meaning of $f (a) = b$ and $g (a) = c$ .

2.

Find the value of $f (a) + g (a)$ .

Takeaways

Common Phrases About Functions

We write:	We mean:

Lesson Summary

In this lesson we interpreted function notation to match features with functions. We learned common phrases that can be used to “translate” function notation depending on the context. For instance, $f (3) = 7$ can be interpreted as the height of the graph at $x = 3$ is $7$ or that when $x = 3$ is substituted into $f (x)$ , the output is $7$ .

Retrieval

Find the indicated function values.

1.

$f (x) = 5 x - 3$

a.

$f (2) =$

b.

$f (x) = 32, x =$

c.

$f (- 8) =$

2.

Graph of $g (x)$ :

a.

$g (2) =$

b.

$g (x) = 4, x =$

c.

$g (- 1) =$

Determine whether the following statements represent a discrete or continuous relationship. Be ready to explain why.

3.

The amount of water in a pool that is being emptied.

4.

The number of runs scored at a baseball game.