Question

question 6 of 10, step 2 of 2
consider the following relation.
step 2 of 2: determine if the relation is a function. if it is not, identify two ordered pairs as proof.
( y = 1 )

Explanation:

Step1: Recall function definition

A relation is a function if every input ($x$-value) has exactly one output ($y$-value). We use the vertical line test: a vertical line drawn anywhere on the graph intersects the graph at most once.

Step2: Analyze the relation $y=1$

The graph of $y=1$ is a horizontal line. For any $x$-value, the $y$-value is always 1. For example, take $x=1$ and $x=2$:

• When $x=1$, $y=1$, so the ordered pair is $(1, 1)$
• When $x=2$, $y=1$, so the ordered pair is $(2, 1)$

Each $x$-value has only one corresponding $y$-value, so the vertical line test passes.

Answer:

The relation $y=1$ is a function. For any $x$-value, there is exactly one $y$-value (1); example ordered pairs: $(1, 1)$ and $(2, 1)$ (any two ordered pairs with different $x$-values and $y=1$ are valid proof).