Question

settle a dispute
jenna and monroe are having an argument. jenna insists the domain for the graph to the left is $-1 < x < 2$ and monroe says it should be $-1 < x \leq 2$. who is right and why?
jenna monroe
explain your thinking.

Explanation:

To determine the domain, we analyze the graph's endpoints. The left endpoint is an open circle at \( x = -1 \), meaning \( x > -1 \) (since open circles exclude the point). The right endpoint is a closed dot at \( x = 2 \), meaning \( x \leq 2 \) (closed dots include the point). So the domain is \( -1 < x \leq 2 \), which matches Monroe's claim.

Answer:

Monroe is right. The left end of the graph has an open circle at \( x = -1 \) (so \( x > -1 \)), and the right end has a closed dot at \( x = 2 \) (so \( x \leq 2 \)). Thus, the domain is \( -1 < x \leq 2 \), supporting Monroe's statement.