Algebra

[fanana0]

Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”.

For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”.

Does this equation determine a relation between x and y? Can the variable x can be seen as a function of y, like x=g(y)? Can the variable y be expressed as a function of x, like y= h(x)? If these are possible, then what will be the domains for these two functions? What are the graphs of these two functions?

Are there points of the coordinate axes that relate to (0, 2) by means of R?

Show work

 

[Dr.Peterson]

Consider the equation and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”.

For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other words: “(x, y) satisfies this equation , if and only if, (x, y) R (0, 2)”.

Does this equation determine a relation between x and y? Can the variable x can be seen as a function of y, like x=g(y)? Can the variable y be expressed as a function of x, like y= h(x)? If these are possible, then what will be the domains for these two functions? What are the graphs of these two functions?

Are there points of the coordinate axes that relate to (0, 2) by means of R?

Show work

Is all of this an exercise you were given, or is part of it your own questions?

Assuming the former, we need to see your own thoughts. If there are parts you don't understand, point them out and tell us what confuses you about them.

There are some odd things in some of the wording; for example, R is a relation between two points, not between x and y, so the relation they are asking about is not R itself, and it's unclear why they talk about a relation R at all. (And R should be described as "has distance 1 from".)

But the actual questions are straightforward ones about the definitions of relation and function.