Functions can be a confusing topic in math; they include different sets that can be easily mixed up. A class discussion helped me to visualize and understand the true meaning of functions. The two sets that a function includes are the domain and the range. The domain is simply the first set of data and the range is the second set of data. A function must also include a rule or relation between the sets that assigns each element of the first set to exactly one element of the second set. This may sound confusing, but if you draw an arrow diagram it helps to break down the relation. The topic of our class discussion was grocery shopping; we chose items for our first set (domain) and prices for our second set (range). The items included ramen noodles, milk, eggs, and lucky charms. The prices included $0.10, $3.59, $3.59, and $2.99. An arrow diagram is used to show the relation between the items and the prices; therefore, the ramen noodles has an arrow to $0.10, the milk and eggs have an arrow to $3.59, and the lucky charms has an arrow to $2.99. The arrow diagram is a great way to picture the relation between items (domain) and prices (range).
Function notation can be another confusing topic, but it is actually a simple concept if you break down what it means. A function notation is relating an input to an output. For example there are two functions: the scanner at Meijer grocery store and the scanner at Walmart. Although they are both working as a “function” the outputs can be different. This means if I scan a gallon of milk at Meijer the output (price) can be different than the output (price) at Walmart. The function notation for this example is f: scanner at Meijer and g: scanner at Walmart; f(milk)=$3.59 and g(milk)=$3.49. The milk is the input and the $price is the output.
An activity we did in class that helped me to better understand function notation was “guess the function”. There were three volunteers that were given a function and the class had to guess what the function was. For example a function was f(x)=3x-1, the class continued to guess the inputs and the volunteers wrote the outputs; the (x) is the input and the 3x-1 is the output. This looked something like: f(2)=5, f(6)=17, f(4)=11, f(10)=29, and f(3)=8. The activity helped to show that function notations can be simple!