1. Chapter 2: Functions and Relations Section 2-3: Functions in the Real World

2. Objective  Given a situation from the real world in which the value of one variable depends on the value of the other, sketch a reasonable graph showing this relationship.

3. Example 1:  Your height depends on your age.  When the sentence says “depends on” it means that in this case, height is the dependent variable (which will always go on the y axis) and age is the independent variable (which will always go on the x axis). age height *Note: The graph does not start out at the origin because when you are born, your height is not 0 inches (usually its around 20 inches). You grow a lot as a baby and then start to steady off before hitting another growth spurt when you are a teenager. Eventually, there will come a time where your height will no longer increase (for some it may even slightly decrease in old age.)

4. Example 2:  The time it takes you to get home from the football game and the speed you drive are related to each other.  When the sentence says “related to” instead of “depends on” we need to determine the independent and dependent variables ourselves.  In this case, the time it takes to get home depends on how fast we drive. speed time *Note: This graph indicates the slower you drive, the more time it takes to get home. The graph starts out close to the time-axis (where speed would be 0) but never touches the axis because if you are driving home, your speed will not be zero. The same thing happens for the speed-axis. The time will get closer and closer to zero but never equal to zero because no matter how fast you are driving, it will still take some time to get home.

5. Asymptote  An asymptote is a line which a graph gets arbitrarily close to, but never touches, and the independent or dependent variable gets very large (in the positive or negative direction)  On the last slide, there were asymptotes on both axes— speed and time can both get very close to (but never equal) to zero.

6. Example 3:  The amount of money you pay for a box of baseballs is related to the number of baseballs in the box.  Here, $ depends on # of baseballs. # of baseballs $ *Note: The line is dotted this time because baseballs can only be sold in a whole number amount (it would not make sense for example to by 2.5 baseballs). Whenever the dependent variable can only be a whole number value, we will always indicated this by a dotted line.