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MANDMO 91 · Sep 2, 2008, 01:33 PM

I am doing some functions review but I forget how to determin if it is a relation when given an equation
help me please!!

y=-3x +5

y=square root of (3x - 1)

Unknown008 · Sep 2, 2008, 10:24 PM

Don't quite understand what you want here...

l_byl · Sep 10, 2008, 10:13 AM

the relation is a function if when graphed it passes the vertical line test aka no two points have the same x value

ebaines · Sep 10, 2008, 10:28 AM

An equation represents a function if for any $x$ in the function's domain there is preciely one value of $y$ that emerges. If there is more than 1 possible value of $y$ for any $x$ , then the equation is not a function.

Example: consider the equation $y=2x$ . The domain for $x$ is $- \infty < x < + \infty$ . For any $x$ , there is only one value of $y$ that comes out of the equation. For example y(2) = 4, y(-10) = -20, etc. Therefore $y= 2x$ is a function.

Another example: consider $y = \sqrt x$ . Here $x$ is in the domain $0 \le x < \infty$ . For $x$ equals zero there is one value of $y$ : zero. But for any positive $x$ there are two values of $y$ , since the square root of a positive number number is either plus or minus. For example, $\sqrt 4 = \pm 2$ . Hence $y= \sqrt x$ is not a function.

Hope this helps.

Unknown008 · Sep 11, 2008, 03:46 AM

You mean that functions are the equations having an inverse, that is, are one one? Ok, but I thought that all equations could be represented as functions, but some of which had inverse, and others don't. K, thanks for the specification ebaines.

ebaines · Sep 11, 2008, 05:36 AM

Originally Posted by Unknown008

You mean that functions are the equations having an inverse, that is, are one one? .

Not quite. Consider the equation f(x)= sin(x). This is defintely a fuction since for any value of x there is precisely one value of f(x). Its inverse is g(x) = arcsin(x), which is not a function, as for any value of x there are an infinite number of values for g(x), for example arcsin(0) = 0, pi, 2*pi, 3*pi, etc.

Unknown008 · Sep 12, 2008, 03:37 AM

Oh, OK, thanks then, your really a help ebaines. Btw, my school is ebene, having the same pronunciation as your username, tee hee!