Problem 53 - Introductory Algebra for College Students

Question

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. My height is a function of my age.

Step-by-Step Solution

Answer

The statement 'my height is a function of my age' only partially makes sense. It makes sense from birth until early adulthood because a person generally grows taller as they age. However, after reaching maturity, one's height usually does not change even as they continue to age. Therefore, beyond early adulthood, height is no longer a function of age.

Step 1: Define the Variables

First, define the variables used in the statement. In this case, 'height' and 'age' are the variables. 'Height' is the dependent variable and 'age' is the independent variable.

Step 2: Understand the Relationship

Next, understand the relationship between the variables. Age and height do have a relationship as a person grows taller as they age, especially during childhood and adolescence. However, after a certain age (typically early adulthood), a person's height generally stays the same even as they continue to grow older.

Step 3: Determine if it's a Function

Finally, determine whether the statement defines a function. A function is a relation where each input (in this case, age) has exactly one output (in this case, height). So, from birth until early adulthood, height can be considered a function of age because for every age, there is typically one corresponding height. However, after reaching maturity, height no longer changes with age. Therefore, the statement 'my height is a function of my age' only partially makes sense. It makes sense until early adulthood.