Hello agent2421 Originally Posted by

**agent2421** Can someone please help me out. This is what I have to do:

- List the key features of the graphs above. Include domain, range, period, and the existence of asymptotes.

for a) y = arccosx

b) y = arctanx.

__Work I've done: __
A) Arccos x

Domain: -1 ≤

*x* ≤ 1

Range: 0 ≤ arccos

*x* ≤ π

B) Arctan x

Domain: xER

Range: -π/2 ≤ arctan

*x* ≤ π/2

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What I need help with:

I don't know how to do the period or the existance of asymptotes ... can you help me with one of them and show how you did it so I can do it for the other graph?

thanks

I agree with your answers so far to question A (although strictly speaking you should describe the domain and range using set notation, or interval notation).

For question B, be a little more careful in your answer for the range. The domain is the whole of $\displaystyle \mathbb{R}$, but the range does not include the end-points $\displaystyle \pm\frac{\pi}{2}$. So you should write$\displaystyle -\frac{\pi}{2} < \arctan(x) <\frac{\pi}{2}$

A periodic function is one that repeats its values at regular intervals. Do either of these functions do that? If they don't, then you can't meaningfully talk about the period.

An asymptote is a straight line (or sometimes a curve, but usually a straight line) to which a graph gets closer and closer as the graph gets further away from the origin. (Speaking loosely, we might say that it's a 'tangent to the curve at infinity' but don't quote me on that!)

Does the first curve have any asymptotes, then? No.

What about the second one? Yes, there are two asymptotes. They're both horizontal. Can you write down their equations? (Use radians, not degrees, since those are the units you've used to describe the range.)

Grandad