Understanding Functions and Context

Understanding Functions and Context

Assessment

Interactive Video

Mathematics, Information Technology (IT), Architecture

1st - 6th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

This lesson explores how context influences functions by examining graphs. It begins with a review of x-intercepts, explaining their significance and common misunderstandings. The lesson then introduces a volume function derived from a cardboard box model, graphing it to find zeros and understand volume changes. Algebraic and contextual explanations are provided for why the volume is zero at certain heights. Finally, the lesson identifies positive and negative intervals of the volume function, emphasizing the importance of context in understanding functions.

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7 questions

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1.

OPEN ENDED QUESTION

3 mins • 1 pt

What are x-intercepts and how can they be identified on a graph?

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2.

OPEN ENDED QUESTION

3 mins • 1 pt

Explain the significance of the y-intercept in relation to the x-intercept.

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3.

OPEN ENDED QUESTION

3 mins • 1 pt

Describe the process of creating a volume function from a piece of cardboard.

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4.

OPEN ENDED QUESTION

3 mins • 1 pt

How do you determine the zeros of the function V(h) and what do they represent?

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5.

OPEN ENDED QUESTION

3 mins • 1 pt

What happens to the volume of the box when the height is set to 0 inches?

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6.

OPEN ENDED QUESTION

3 mins • 1 pt

How does cutting squares from the corners of the cardboard affect the dimensions of the box?

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7.

OPEN ENDED QUESTION

3 mins • 1 pt

Identify the intervals where the volume of the box is positive and explain why.

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