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- hmmm... How do I know if this is a function or not?
- Well, have you tried to verticle line test?
- What's the verticle line test?
- That's how you can easily test for a function! you take a ruler and run it across the graph, if the graph has two lines that are at the same point it's not a function. Here, let me show you.
- For example, this circle which let's say has a domain of [-10,5] and a range of [-3,10] it is not a function becuase when the ruler goes over it the ruler crosses two lines
- For example, this circle which let's say has a domain of [-5,5] and a range of [-10,10] it IS a function becuase when the ruler goes over it the ruler crosses the line only once all the way across.
- Oh, Okay!
- Okay, I think I'm getting it! So if this is how you express a function then what is function notation?
- Function notation is simply when a function is expressed an equation
- You will also need to do function operations, so take some notes.
- Wow! so for adding functions you add like terms, for subtracting functions you subtract like terms, and for multiplication you do F.O.I.L.?
- Finally you'll need to know how to multiply functions. Let's say that we have p(x) times k(x) with p(X) being equal to x^2+1 and k(x) being equal to x-5. From here you'll have to do F.O.I.L. which means to multiply the first (x^2 times x), outside (x^2 times -5), inside (1 times x), and last (1 times -5). After you multiply all those pairs you should get x^3-5x^2+x-5
- for subtracting you take two functions, lets say h(x) - g(x) with h(x) being equal to x+5 and g(x) being equal to x^3 + x -1. This would look something like this: (x +5) - (x^3 + x -1). You need to distribute the negative as if it were a number to the second set of numbers and by doing that the x's should cancle out and adds 1 to the 5 because the negative 1 is now positive. So you should end up with the answer -x^3 + 6
- for adding you take two functions lets say f(x) + g(x) with f(x) being equal to 3x-2 and g(x) being equal to x^3+x-1. From there you add(3x-2)+(x^3+x-1) -- 4x-3+x^3 -- x^3+4x-3
- Thanks!
- That's right!
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