<p>Can someone really good at math explain functions to me. Mainly function notation and evaluation, Domain & range, functions as models, linear/ quadratic functions, et cetera.</p>
<p>I guess I’ll try.</p>
<p>What a function basically is is an equation where you plug in a number (x) BUT YOU ONLY EVER GET ONE NUMBER OUT (y). </p>
<p>Alright so function notation is usually as follows:</p>
<p>f(x)=x+9</p>
<p>in other words this is just y=x+9 but in function notation. It just makes it easier to know what you plugged in the first place. Like, for example, if I wanted to know what would happen if I plugged in a 9, I would say f(9)=9+9=18</p>
<p>So f(9)=18</p>
<p>See, it makes a lot more sense than just y=18 which doesn’t tell you what the number was plugged in in the first place.</p>
<p>This is what evaluating is btw. If you wanted to evaluate f(2), you plug in 2 for x. </p>
<p>So in a function, the domain is all the x values and the range is all the y values.
There is only one range for every domain.</p>
<p>Linear functions is where the x term of highest degree is one.
Ex. f(x)=x+3
f(x)=4x-7</p>
<p>Quadratic functions is where the x term of highest degree is two.
Ex. f(x)=x^2+4x+4</p>
<p>This probably was of no help, but I sort of tried. :(</p>
<p>So in other words 5 would be a domain because it is …
f(x)=x^3 +(10/x) , f(5). and the ouput number is the range, right? f(5)=127. 127 is the range, right?</p>
<p>Nearly, but not quite.</p>
<p>The domain is the set of all numbers that you can put into the function and get an answer back. Five is an element of the domain, or in the domain, for the function f that you have defined, because if you plug in 5, you get an answer: f(5) = (5)^3 + 10/(5) = 127. Zero, by contrast is not in the domain of f, because when you try to substitute 0 for x, you get (0)^3 + 10/(0), and dividing 10 by zero does not give a real answer (or even a complex one, for that matter). But we don’t say “5 is a domain.” The domain is the whole set of possible inputs. And the domain for the function f in your example is all real numbers except 0. You can plug any non-zero real number into the function where “x” is and get a real answer back.</p>
<p>Similarly, the range is the set of all numbers that you can get as a result when you plug numbers into a function. Because in your example, f(5) is 127, 127 is an element of the range, but we don’t say that “127 is a range” of the function.</p>