Analyzing Graphs

Unit 2: Functions and their Graphs

​

2.5 Graph Characteristics​

​Some text here about the topic of discussion.

1. Critical Points-

   points w​here the function changes slope or sign.

2. Extrema-

   points where the function changes direction (sign).​

3. Point of Inflection​-

   point where the function changes slope, but not sign.​

​

​Some text here about the topic of discussion.

1. Vocabulary

​

​ https://www.desmos.com/calculator/el9jwncb8d

Multiple Choice

How many extrema are there in this graph?

• 2 max, 2 min

• 3 max, 2 min

• 2 man, 3 min

• 3 increasing intervals, 2 decreasing intervals

• 2 increasing intervals, 3 decreasing intervals

Multiple Choice

How many extrema (max and mins) are in the picture?

• 2

• 3

• 4

• 5

Multiple Choice

Minimum or maximum?

• Minimum
• Maximum

Multiple Choice

How many critical points does this function have?

• 0

• 1

• 2

• 3

4. Relative Maximum-

   a high point in the graph compared to values around it.​

5. Absolute Maximum-

   the highest point anywhere on the graph.​

6. Relative Minimum-

   a high point in the graph compared to values around it.​​

7. Absolute Minimum-​

   the lowest point anywhere on the graph.​

​ https://www.desmos.com/calculator/u0vbqz9m4x

​ https://www.desmos.com/calculator/oa3507zetn

Multiple Choice

This graph has an Absolute Maximum Point.

• True

• False

• Cannot be determined

Multiple Choice

Which of the following does this graph not show?

• absolute max
• absolute min
• relative max
• relative min

Multiple Choice

The function shown has an Absolute Minimum.

• True

• False

• Cannot be determined

Multiple Choice

The function shown has an Absolute Maximum.

• True

• False

• Cannot be determined

Multiple Choice

How many Critical Points does this function contain?

*points at which the graph changes direction..

• 2 Critical Points

• 3 Critical Points

• 4 Critical Points

Multiple Choice

This graph contains an Absolute Maximum Point.

• True

• False

• Cannot be determined

Multiple Select

Which point(s) are considered relative minimum points?

• (-3,0)

• (-2,40)

• (1,-175)

• (4,0)

8. Increasing Behavior-

   Moving from left to right, any interval where the slope is positive.

9. Constant Behavior-

   Any interval where the slope is zero.

10. Decreasing Behavior-

    Any interval where the slope is negative, moving from left to right.

​

​Some text here about the topic of discussion.

​https://www.desmos.com/calculator/xqcqzeiuan

Multiple Choice

What is the increasing interval for the function below?

• $$\left(-\infty,\infty\right)$$

• $$\left(-\infty,2\right]$$

• $$\left(-\infty,6\right]$$

• $$\left(-6,6\right)$$

Multiple Choice

What is/are the increasing interval(s) for the function shown?

• $$\left(-3,\ 1\right)$$

• $$\left(4,\ 8\right)$$

• $$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$$

Multiple Choice

What is the decreasing interval(s) on the function shown?

• $$\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$$

• $$\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$$

• $$\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$$

• $$\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$$

Multiple Choice

What is the decreasing interval(s) on the function shown?

• $$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$$

• $$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$$

• $$\left(-\infty,\ -2\right)\ and\ \left(0,\ 2\right)$$

• $$\left(-2,\ 0\right)\ and\ \left(2,\ \infty\right)$$

Multiple Choice

Over what interval is this function constant?

• -5 < x < ∞
• -3 < x < 4
• 4 < x < ∞
• -5

Multiple Choice

When is the velocity decreasing?

• 0 < t < 60
• 40 < t < 60
• 15 < t < 40
• -40 < t < 0