1. function graphs

How would I graph these two functions on a calculator?
I need to find domain, range, zeros, etc., along with a sketch of graph. Or would it be easier to graph by hand? how? Thanks!

$f(x) = log_2x$

$f(x) =\sqrt{a^2-x^2}$

2. Originally Posted by live_laugh_luv27
How would I graph these two graphs on a calculator?
I need to find domain, range, zeros, etc., along with a sketch of graph. Or would it be easier to graph by hand? how? Thanks!

$f(x) = log_2x$

$f(x) =\sqrt{a^2-x^2}$
The first one can be put in as $\frac{\log{x}}{\log{2}}$ into the calculator

The second one is no good with a calculator because there are two variables. Sketch it by hand and you can find intercepts that depend on the value of a (y=0 at x=a,-a and x=0 when y=a). You can find the domain by making sure the what is under the radical is $\geq 0$ and you can find the range by solving the equation for x, and then finding the domain of that new function (you are finding the domain of the inverse function)

3. Originally Posted by artvandalay11
The first one can be put in as $\frac{\log{x}}{\log{2}}$ into the calculator

The second one is no good with a calculator because there are two variables. Sketch it by hand and you can find intercepts that depend on the value of a (y=0 at x=a,-a and x=0 when y=a). You can find the domain by making sure the what is under the radical is $\geq 0$ and you can find the range by solving the equation for x, and then finding the domain of that new function (you are finding the domain of the inverse function)
Hello : thank you
I"think a is the parameter no variable.

4. Originally Posted by live_laugh_luv27
How would I graph these two functions on a calculator?
I need to find domain, range, zeros, etc., along with a sketch of graph. Or would it be easier to graph by hand? how? Thanks!

$f(x) = log_2x$

$f(x) =\sqrt{a^2-x^2}$
the second one

$y=\sqrt{a^2-x^2}$ it is the upper semi circle of the circle $y^2+x^2=a^2$ intersect with the x-axis at the points x=a and x=-a

5. Originally Posted by Amer
the second one

$y=\sqrt{a^2-x^2}$ it is the upper semi circle of the circle $y^2+x^2=a^2$ intersect with the x-axis at the points x=a and x=-a
ok..How would I set up the axes?

6. Originally Posted by live_laugh_luv27
ok..How would I set up the axes?
like this

I need to find domain, range, even/odd etc.

8. Originally Posted by live_laugh_luv27

I need to find domain, range, even/odd etc.
Treat a like a real number

Domain $0 \leq a^2-x^2 \Rightarrow -a\leq x\leq a$

Range $x^2+y^2 \leq a^2$ with $0 \leq y \leq a$

f(x)=f(-x) so the function is even

9. Originally Posted by Amer
Treat a like a real number

Domain $0 \leq a^2-x^2 \Rightarrow -a\leq x\leq a$

Range $x^2+y^2 \leq a^2$ with $0 \leq y \leq a$

f(x)=f(-x) so the function is even
wow, can't believe I didn't see that. Thanks!