Function Notation - Problem 1
Function notation, f(x) or "f of x", is the same as "y". Function notation is used to indicate that one variable, "f(x)", is a function of the other variable, "x". Write a function using the information given in the word problem. Next, evaluate the function with specific values for the variable by plugging, or substituting, in the value and solving.
A lot of times students are intimidated by word problems and to be honest I sometimes get intimidated also. But one thing that can really help is that you write the word problem in what's called the function notation. So let's check this one out.
Rudy earns $25 per hour in his summer job. Damn way to go Rudy. Write a function f(x) to describe his earnings. Evaluate your function when x equals 5 hours and how many hours did he work if he earned $150?
All right let's do it, f(x) to describe his earnings. F(x) is just the same thing as if I were to write y equals something but the reason why we use f(x) is to show how much money he earns is the function of how many hours he works.
So let's see the amount of money he gets is 25 times the number of hours he works. If he works one hour he would earn 1 times 25 he would earn $25. That's how this works. Your x number represents number of hours worked which makes sense in part B.
Evaluate your function when x equals 5 hours. Okay so instead of f(x) now x is equal to 5 so I'm going to write f(5) that's going to be 25 times 5 and that looks like kind of tricky because there's 5's everywhere all of a sudden. What happened is I just stuck 5 in there for x right there and also 5 for x right there to represent 5 hours. Well this means mathematically is on finding the value of the output when the input number was 5. So 5 times 25 is $125 so we would say f(5) equals 125.
The thing I like about function notation is we can see not just the answer like 125 but I can see when I out in the input value of 5, I got my output of 125. I think that's kind of a nice for me at least to remember what I did to get that answer.
Okay last but not least how much did he work if he earned $150? Well we know his earnings is equal to 25 times hours worked, so we set it up like that 150 equals 25x and then what you would do to solve for x is to divide both sides by 25 and you end up getting x equals 6 hours.
Please be sure to label your answers, don't just write x equals 6 or f(5) equals 125. Be really careful to stick the dollar sign in there and the word hours so you remember that this is a problem that relates to a real world situation like that's the whole point of Math, like relax Math really does apply to the real world I promise. If you can help remind yourself to write that kind of stuff down.
So the last thing I want to leave you with is just remembering that even though function notation is new and kind of weird because you have the whole of 'f' thing it's pretty cool because you can see what input value you put in, in order to get your output value. That's what I personally like about function notation.