Common Core Standards: Math
2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Students should know that function notation isn't as difficult as they think. In fact, it's downright easy. Much easier than, say, learning French. Nous faire confiance.
All they have to do is isolate an equation for y and then replace it with f(x) (read as "f of x"). That's pretty much it.
The function rule is the equation that represents the unique output values. In other words, it explains what's done to the input value to make it the output value. For instance, a function rule can be, "Multiply the input value by 2 and then subtract three from it." We could write this function rule as f(x) = 2x – 3.
For an equation to be a function, x is the independent variable and the y value (or f(x) value) is the dependent variable. This makes sense, since the output value depends on the input value. D'accord?
The plus side about function notation is that we can write the input and output of a function in one line. Let's say the input of x = 2 makes an output of f(x) = 1. Rather than writing each one separately, we can simply say f(2) = 1. To make sure your students remember this, emphasize that the input is 2 because it's in the parenthesis.
Once students are proficient in using this notation, they can begin to apply it to real-life problems. They should also make sure to use function notation consistently. Practice makes perfect, oui?
For instance, a French real estate agent's weekly earnings can be calculated as the output of €400 plus 6% of his weekly commission. This should be interpreted as the function f(x) = 400 + 0.06x. If the students are asked to find the agent's earnings after his weekly sales are €46,900, they should know that they're being asked to find f(46,900), or f(46,900) = 3,214. Ooh la la!