Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 13, 2024

Find the possible values of $x$ and $y$ for two distinct points, $(5, -2)$ and $(x, y)$ , to represent a function.

STEP 1

Assumptions
1. A function is defined such that for each input (or $x$ -value), there is exactly one output (or $y$ -value).
2. The points given are $(5, -2)$ and $(x, y)$ .
3. The points represent a function, meaning no two points can have the same $x$ -value with different $y$ -values.

STEP 2

To ensure that the two points represent a function, the $x$ -values of both points must be distinct. This is because a function can only have one output for each input.

STEP 3

Since the first point has an $x$ -value of 5, the second point must have an $x$ -value different from 5.
$x \neq 5$

STEP 4

For the $y$ -value, there are no restrictions in a function other than the one related to the $x$ -value. This means that $y$ can be any real number.
$y \in \mathbb{R}$

STEP 5

Therefore, the possible values of $x$ and $y$ for the second point $(x, y)$ to represent a function along with the point $(5, -2)$ are:
The value of $x$ can be any real number except 5. The value of $y$ can be any real number.

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