Lesson 3.5: Intervals of Increase and Decrease

Lesson 3.5

Intervals of Increase and Decrease​

By Reed Carbone

Definition:

​Increasing Function: A function is increasing when its slope is positive. (i.e. the line is pointing up)

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Decreasing Function: A function is decreasing when its slope is negative​. (i.e. the line is pointing down)

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Interval: An interval is like a certain part of a graph. For example, if I want to look at just the parts of a graph from x = 0 to x = 3, then this would be an interval.​

Subject | Subject

Some text here about the topic of discussion

​Visuals:

​Give the intervals the function is increasing and decreasing:

Multiple Choice

Is the function increasing or decreasing?

• Increasing

• Decreasing

• Both

• Not enough information to determine

Multiple Choice

Is this function increasing or decreasing?

• Increasing

• Decreasing

• Increasing and Decreasing

• Neither

Multiple Choice

What intervals is this function increasing?

• -2 to 2

• 0 to 1

• -1 to 1

• 0 to 2

Multiple Choice

What intervals is this function decreasing?

• -3 to 3

• 0 to 3

• 1 to 3

• 2-3 to 0

Multiple Choice

What intervals is this function increasing?

• 0 to 360

• 90 to 270

• 0 to 90 and 270 to 360

• 0 to 90 and 180 to 270

How to sketch a function:
Keep track of clues from the context of the problem to determine if the graph should be increasing, decreasing or constant and the duration of the interval.

Jax is riding his bike to school. He starts at home and rides to school for 1 hour. He then stays at for 6 hours. When he leaves he notices he popped a tire and he has to walk his bike home for 2 hours. Sketch this function that tracks his distance from home and time in hours.

Draw

Melody starts at her house and rides her bike for 10 minutes to a friends house. She then stays at her friends house for 60 minutes. Sketch the graph that models her distance from home and time.

Draw

Aaron's mother drives to the gas station and fills up her tank. Then she drives to the market. Sketch a graph to model the gas in her tank over time.

​Conclusion: Write two complete sentences about what you learned today.