Interpolating and extrapolating information Interpreting graphs Interpolating and extrapolating information

What we can all do with graphs When you have a graph, you can do all sorts of things You can create an equation based on the information. Often this can be easier if we create a table of values to help. We can interpolate missing information. This means that we can estimate a value within given data. We can also extrapolate missing information. This means we can estimate a value beyond the given data.

interpolating Remember, interpolating means estimating information within the given data. That means you must estimate between at least two known values. Interpolating on a graph is easy to do, and it is very visual. Let’s try it with an example

interpolating A weather balloon is recording air temperatures at different altitudes. The data is approximately a linear relation. Here is the table: First, we need to draw a graph. altitude temperature 350 11.4 750 5.7 1000 2.1 1500 -5 1800 -10

interpolating Here is the graph: What if we wanted to know the temperature at 600 meters? We need to draw two lines: a vertical one from 600 to the graphing line A horizontal one from that intersection point to the y axis. We discover that at 600 meters, the air temperature is approximately 8 degrees

Interpolating Remember our graph: What if we wanted to know how high the balloon was if the temperature was reading -7.5 degrees? We would have to draw a horizontal line from -7.5 until it intersects the graphing line. Then we would draw a vertical line from that point to the x axis. We would discover that the balloon was at approximately 1700 meters altitude.

Extrapolating Remember, extrapolating means that you are estimating a value beyond a given set of values. Using our weather balloon graph, extrapolate the altitude of the balloon when the temperature reads: 15 degrees -15 degrees How??? Extend the graphing line beyond the known values (with a dashed line)

A word of advice Interpolating and extrapolating should only be used when it makes sense to do so. Sometimes, it’s just not reasonable to have values between or beyond the values on a graph.

Homework: Page 226 and 227 4, 5, 7, 8, 9,11