1B. Functions and Function Notation
Instructions:
- Use the input box for to input a function formula. Use the input boxes for and to set the endpoints of the domain of . This just helps to narrow down some calculations that the computer will have to do in this application.
- Use the checkbox for "Evaluate" or "Solve" one at a time to see the process for evaluating or solving a function, respectively.
- Evaluate: Use the slider tool for to adjust the input value. Think of as a constant -value that we are free to choose. Then use the unlabeled black slider tool to observe the visualization for evaluating a function. When you want to switch to "Solve," uncheck the checkbox for Evaluate to keep the graph from becoming too cluttered.
- Solve: Use the slider tool for to adjust the output value. Think of as a constant -value that we are free to choose. Then use the unlabeled black slider tool to observe the visualization for solving a function. When you want to switch to "Evaluate," uncheck the checkbox for Solve to keep the graph from becoming too cluttered.
Functions and Function Notation:
A function is a set of ordered pairs that satisfies a special condition: each x value can only be paired with one y-value. (This condition is often visualized with the Vertical Line Test.) This condition allows us to think of a function as an input-output relationship. When you plug in an input (x), you can only get one output (y). This input-output relationship is expressed as:
which is read as "f of x equals y." The input is called the independent variable, and the output is called the dependent variable. Typically the quantity represented by somehow depends on the quantity represented by . This means we can think of it like a change in the value of causes a change in the value of .