27 given the relation $r = {(-1,1),(0,3),(-2,-4),(x,5)}$. state a value for $x$ that will make this relation…

Explanation:

Step1: Recall function definition

A relation is a function if each input (x - value) has exactly one output (y - value).

Step2: Identify existing x - values

The existing x - values in the relation $R={(-1,1),(0,3),(-2,-4),(x,5)}$ are $-1$, $0$, and $-2$.

Step3: Determine valid x - value

To make the relation a function, $x$ can be any real number except $-1$, $0$, and $-2$. Let's choose $x = 1$.

Step4: Explain why it's a function

Since $x = 1$ is not equal to $-1$, $0$, or $-2$, each input value in the relation ${(-1,1),(0,3),(-2,-4),(1,5)}$ has a unique output value.

Answer:

$x = 1$ (any real - number except $-1$, $0$, and $-2$ would be correct)