Chapter 8.1, Problem 17E

a.

To determine

Do the ordered pairs $\left(\text{age,height}\right)$ represent a function? Explain.

Answer to Problem 17E

Yes, the ordered pairs $\left(\text{age,height}\right)$ represent a function.

Explanation of Solution

Given:

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

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.

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.

To determine

Would you expect the ordered pairs $\left(\text{height,age}\right)$ to represent a function? Why or why not?

Answer to Problem 17E

No, the ordered pairs $\left(\text{height,age}\right)$ don’t represent a function.

Explanation of Solution

Given:

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

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 out-put.

Therefore, the ordered pairs $\left(\text{height,age}\right)$ don’t represent a function.