Graphical Analysis questions?

Question

First, I've been asked to graph multiple functions, 2 of which I cannot figure out how to graph or enter into a calculator for a general idea:

f(x)= log base 2 (x) ; f(x)= √(a^2)-(x^2) )

So if somebody could explain how to do this, or find a reference I can check out that would be awesome.

Secondly, Is there a relationship between symmetry in a function's graph and the function being even or odd?

Last, if a set of directions say to "Draw a reflection" of..sin(x) (for example), is that the same as regular graphing?

Thanks

For the log base 2 (x)

It's like log-subscript 2 (x)

Answer 1

For logbase2(x), this will be equal to log base 10 or natural log times a constant (I'll let you figure out what that is.) You're not going to be able to plot anything without a numerical value for a in the second equation.

An even function is symetric about the y axis.
An odd function is antisymetric about the y axis (-reflection thru y)

Since sin is odd, a reflection through the y axis is -sin from -ininity to 0 and sin from 0 to infinity.

Yeah, I know what it is; see above. For example:

log(x) = log(e)*ln(x)

A similar strategy will allow you to link log base 2 to the two common bases, either ten or e, your choice.