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Q17.

Expert-verified

Pre-algebra

Found in: Page 404

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

The height of a person is measured every year from the age of 1 year to the age of 50 years.
Do the ordered pairs $(age, height)$ represent a function? Explain.
Would you expect the ordered pairs $(height,age)$ to represent a function? Why or why not?

Yes, the ordered pairs $(age,height)$ represent a function.
No, the ordered pairs $(height,age)$ don’t represent a function.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

a. Step 1. Given Information.

The height of a person is measured every year from the age of 1 year to the age of 50 years.

Step 2. Calculation.

We know that a function is a relation, where each input in the domain has exactly one specific corresponding output.

In the ordered pair $(age,height)$ , age is independent and height is dependent variable.

We know that as we grow older, our height also increases. After a specific age, the height ceases to increase.

We also know that for a relation to be a function, one x-value cannot have two y-values, while two x-values can have same y-value.

Step 3. Conclusion.

Since for a relation to be a function, two or more values of independent variable can have same out-put, therefore, the ordered pairs $(age,height)$ represent a function.

b.Step 1. Given Information.

The height of a person is measured every year from the age of 1 year to the age of 50 years.

Step 2. Calculation.

We know that a function is a relation, where each input in the domain has exactly one specific corresponding output.

In the ordered pair $(height,age)$ , height is independent and age is dependent variable.

We know that as we grow older, our height also increases. After a specific age, the height ceases to increase.

We also know that for a relation to be a function, one x-value cannot have two y-values, while two x-values can have same y-value.

Since height ceases to increase after a specific age, so a person will have same height at different ages that is an input will have more than one output.

Step 3. Conclusion.

The ordered pairs $(height,age)$ don’t represent a function.

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