Writing f(x) format of equations

[dogtrainer]

Homework Statement

How do you write the following in f(x) form? x =1; {3<y<6}
and (x – 3)2 + (y – 9)2 = .25

Homework Equations

The Attempt at a Solution

I had to use these equations in a project that I am graphing and I must also include the f(x) form and I am lost. Can you please help? My project is due tomorrow? I have 6 other equations to put in the f(x) format, but I figured if I could get help on these two I should be able to figure out the others.

 

[rs1n]

Writing it in f(x) form is (for the sake of simplicity) essentially solving for y (i.e. isolating y so that it is on one side of the '=' sign and everything else that DOES NOT CONTAIN y is on the other side of the '=' sign. For example:

$$(x - 3)2 + (y - 9)2 = .25 \implies y = \frac{.25-(x-3)2}{2} + 9 \implies f(x) = \frac{.25-(x-3)2}{2} + 9$$

Generally speaking, one can only obtain the form "$$f(x) = \dotsm$$" if the graph is a function (passes the vertical line test). The problem with your first example: $$x=1; \{ 3 < y < 6\}$$ is that the graph is not a function (it's a vertical line segment).