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Expert-verified Found in: Page 404 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # 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 $\left(\text{age},\text{height}\right)$ represent a function? Explain.Would you expect the ordered pairs $\left(\text{height,age}\right)$ to represent a function? Why or why not?

1. Yes, the ordered pairs $\left(\text{age,height}\right)$ represent a function.
2. No, the ordered pairs $\left(\text{height,age}\right)$ don’t represent a function.
See the step by step solution

## 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 $\left(\text{age,height}\right)$, 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 $\left(\text{age,height}\right)$ 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 $\left(\text{height,age}\right)$, 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 $\left(\text{height,age}\right)$ don’t represent a function. ### Want to see more solutions like these? 