Lesson 6 Be the Change Practice Understanding

Learning Focus

Determine if a relation is linear, exponential, quadratic, or some other kind of function.

Determine the type of growth and key features of the function.

What characteristics of each representation make it easy to identify the function type?

Open Up the Math: Launch, Explore, Discuss

Today’s lesson is a card sort activity to show what you know about quadratic functions. The instructions are:

Lay out the set of A cards that show a representation of a different function on each card.
Select any B card. The B cards are the same functions as the A cards, but different representations.
Match your B card with an A card that shows the same function.
Now that you have two representations of a function, find a C card that has information that matches the function.
Repeat until all the cards are matched in sets of three, an A card, a B card, and a C card.
When all your cards have been matched to one of the C cards, complete the missing information about the functions.

1.

C1 Matches with:

Type of function:

Type of change:

Second difference:

$312.5 < f (55) < 450$

2.

C2 Matches with:

Type of function:

Type of change:

Change factor for an interval of $1$ is $0.85$ .

$f (0) =$ $f (3) =$

In this context, $f (3)$ means:

3.

C3 Matches with:

Quadratic Function

Linear rate of change

$x$ -intercepts: $(- \frac{3}{4}, 0)$ and

$y$ -intercept:

4.

C4 Matches with:

Exponential Function

Type of change:

Domain: ${n | n \in Z, n \geq - 3}$

Range:

5.

C5 Matches with:

Type of function:

Type of change:

Minimum: $(2, 4)$

Interval of decrease:

Interval of increase:

6.

C6 Matches with:

Type of function:

Rate of change:

$f (2) =$

$f (x) = 6$ at $x =$

7.

C7 Matches with:

Linear Function

Constant rate of change:

Domain:

Range: $[55, \infty)$

8.

C8 Matches with:

Quadratic Function

Type of change:

Second difference:

Domain: ${n | n \in N}$

Range:

9.

C9 Matches with:

Quadratic Function

Type of change:

$f (3) =$

$y$ -intercept:

10.

C10 Matches with:

Type of Function:

Linear rate of change

Second Difference:

Domain: $(- \infty, \infty)$

Range:

Ready for More?

Try to create one more representation for each of the quadratic functions. Watch out! This can get tricky.

Takeaways

Finding features of quadratic functions:

Lesson Summary

In this lesson we sharpened our skills in distinguishing quadratic functions from linear and exponential functions. We made connections with equations and graphs of quadratic equations and discussed efficient methods for identifying features of quadratic functions.

Retrieval

Predict how the graph of each function will compare to the graph of $y = x$ . Graph the equations with the line for $y = x$ to see if your predictions are correct.

1.

How does $y = x + 5$ compare to $y = x$ ?

2.

How does $y = x - 5$ compare to $y = x$ ?

3.

How does $y = - 5 x$ compare to $y = x$ ?

4.

Create the explicit function that goes with $f (1) = 12; f (n) = f (n - 1) - 3$ .

5.

Create a recursive rule that represents $g (x) = 5 {(2)}^{x}$ .