Functions (my nemesis)

[Pau]

yo to everyone here~

I'm trying to review my past subject (calculus) since I'm gonna need it in my present one but I can't get past the topic on "Functions" (especially about domains, range, graphing, and maybe the f(x) thing).

example:

let's go with the simple y=x^2.

what is it's domain? range? how is it graphed?

so if anyone can help me review i'd really appreciate it .
thank you!

[Vauxhall]

Well, in functions, "f(x)" is basically what states that it is a function, lol.
When graphing, you can typically think of "f(x)" as the "y" in say "y = mx + c". *shrugs* At least, that's how I thought of it.

In y = x^2, the domain is (-infinity, +infinity) ; range is [0, +infinity)

• Domain = x-values. In this case, it's +/-infinity because the graph keeps infinitely stretching into the positive/negative x-axis
• Range = y-values. It starts at 0 because when you graph it, the graph sits on the baseline, so there are no negative y-values for the graph

And uhhh... You graph with a graphics calculator? xD

[Soraiiya]

oh, this is pretty simple :)

so. domain: the x-values and range: y-values, right? since you're using x^2 as an example, let's go with that.

try plotting a few points. y = x^2. so let's say x = 0. y = 0^2, so y = 0. your first point would be (0, 0).
now try x = 1. y = 1^2, so your second point would be (1, 1).
x = 2. y = 2^2. third point would be (2, 4).

and etc.

you can do negatives too! so try doing x = -1. y = (-1)^2 = (-1, 1).
x = -2. y = (-2)^2. your point is (-2, 4). etc.

now, domain refers to the x-values. notice that your x-values so far are 0, 1, 2, -1, and -2. what does this mean? they are continuously increasing in both directions, right? both positive and negative? this means that the domain is all real numbers.

let's look at the range, which are the y-values. so far your y-values that you've figured out are 0, 1, 4. note that these have no negative numbers, since a negative value squared is positive. therefore, your range would be all POSITIVE real numbers, or y is greater than or equal to 0.

as for graphing it, just plot the points. it should be an open parabola with the vertex at the origin. i hope this helped! 

[Pau]

so that's it....thank you guys~

which reminds me, i was reading this book on functions and I'm on absolute values right now (i.e  |x| )

and I was pretty much wondering what's the difference b/w    x   and   |x|   

[Vauxhall]

Absolute values are pretty much a simplification of numbers.
Say...
| -4, -9, -10 | = 4, 9, 10
and if there's a negative sign in front...
-| -5 | = -5

Refer to this? They explain it pretty well.

[Aurelia]

Graphing wise, everything inside absolute value brackets is positive. So if you have to graph an absolute value function, everything should be above the x-axis.

So say you had a parabola and part of it was underneath the x-axis. When you graph that parabola in an absolute value function, whatever part is underneath the x-axis will be flipped above it.

[Soraiiya]

Oh another thing about graphing absolute value: it generally should be a V-shape, and always above the x-axis. So the graph of |x| should look like a V with the vertex at the origin~

Something like this: