# Math Help - Sqrt Graph Help

1. ## Sqrt Graph Help

How would i graph the sqrt of (a^2)-(x^2)??

2. Hello, Godfather!

How would i graph: . $y \;=\;\sqrt{a^2 -x^2}$ ?

Square both sides: . $y^2 \:=\:a^2-x^2 \quad\Rightarrow\quad x^2+y^2 \:=\:a^2$

This is a circle: center at the origin, with radius $a.$

Then: . $y \;=\;^+ \sqrt{a^2-x^2}$ .is the upper semicircle.

3. how would i graph it without know a ?
what about the domain,range,zero,even/odd,periodic and one to one ?

4. The domain consists of all legal values for x given that the function must be a real number. So, $a^2 - x^2$ must be nonnegative. For what values of x is this true?

The range consists of all the values the function can take on its domain. To start, consider what the largest possible value for $\sqrt{a^2 - x^2}$ would be. Can the function give a negative result?

The zeroes of the function will be the same as the zeroes of $a^2 - x^2$. For what values of x is the function equal to zero?

Whether or not the function is even or odd depends on whether or not $f(x) = f(-x)$ or $f(x) = -f(-x)$, respectively.
Given that $f(x) = \sqrt{a^2 - x^2}$, is either of these statements true?

If the function is periodic with period p, then $f(x) = f(x + np)$ for every integer n. Is a semicircle periodic?

If the function is one-to-one, then every y value must be matched by exactly one x value. Is this the case for a semicircle?