Linear Functions Find the Function Rule Writing Equations

Linear Functions – Find the Function Rule – Writing Equations Algebra One Ms. Hardy

Let’s write our function rules with the official notation: There is a special notation (called ‘function notation’) that is used in writing equations: If the function name is f , and the input name is x , then the unique corresponding output is called f(x). The notation ‘f(x) ’ is read aloud as: ‘ f of x ’.

This notation signals that you have a function…. Usually teachers will just say “f(x) is the same thing as “y” in an equation. ” Well, sort of. But it is more powerful than that…. By writing f(x) you are indicating the result in applying the function rule (equation) is an output or function of x. It’s much more exciting and powerful than just plain old “y”.

Each output in the table is 5 more than twice the input. Write a function rule, then use it to fill in the table.

Writing a Function rule for a problem situation Ex 1: The height of the river starts at 10 feet. During the big storm the height rose by 2 feet per hour. What is a function rule for the height of the river as a function of the number of hours that have passed during the storm?

Writing a Function rule for a problem situation Ex 2: You are at your grandmother’s house which is 40 miles from home. You ride your bicycle home at an average rate of 8 miles per hour. Write a function equation for the number of miles you are from home as a function of hours you have been riding.

Function Rules from Graphs Remember the example of the woman and her car? Let’s try to write an equation…. . Starting value: She is getting closer by how many feet per second?

Later we will be learning some specific rules for writing function equations from graphs. See if you can write an equation for each of these graphs – considering the data points on the graphs….