# Attributes of Functions

#### liana456

##### New member
How can attributes of functions be used in the real world

#### Dr.Peterson

##### Elite Member
Can you narrow this down a little bit? What particular attributes are you referring to?

(And whose real world are you thinking of?)

pka

#### HallsofIvy

##### Elite Member
The "real world" of a person who spends his time saying "Do you want fries with that?" is quite different from that of a professional engineer!

But, what is your understanding of, first, what a "function" is, and, second, what "attributes" a function might have?

#### liana456

##### New member
Hello! I’m so sorry..

By functions I mean like linear graphs, exponential functions, parabola, etc. When I say attributes I mean like minimum value, maximum value, y and x intercepts, vertex, domain, range, etc. What I am asking is how would this information be helpful to someone who works with graphs a lot. How would this info make their work easier and why is this important to know.

Again, I apologize for the vagueness of my initial question.

Thank you so much!

#### JeffM

##### Elite Member
The critical attribute of a function is that it gives a unique answer. It is not ambiguous.

#### Dr.Peterson

##### Elite Member
By functions I mean like linear graphs, exponential functions, parabola, etc. When I say attributes I mean like minimum value, maximum value, y and x intercepts, vertex, domain, range, etc. What I am asking is how would this information be helpful to someone who works with graphs a lot. How would this info make their work easier and why is this important to know.
First, in one sense, none of it matters a lot, since you can just type an equation into a graphing program and get the graph with no effort.

On the other hand, since you can do that, it does matter a lot, because in letting a machine do it, you are missing out on all that you learn by thinking about details like minimum, maximum, increasing, decreasing, and so on. In particular, the grapher may miss details like "holes" where a function is undefined, or things that happen off-screen so you don't notice them.

But why do these things matter? That depends on why you are making the graph; but for example, many applications call for finding a maximum or minimum; the fact that a function is not one-to-one (which tends to go along with having a max or min) can be very important in determining whether there will be a unique solution to a problem; and intercepts are often very important points in an application (e.g. the profit if you don't sell anything, or the time at which a projectile hits the ground.

Ultimately, you'll notice, things about graphs matter not so much in terms of the graph itself, but in terms of the purpose of the graph, the application. But you're learning about these things, not in light of a particular application (which may not even exist yet), but so you'll be ready for whatever you end up needing them for.