Question

1. the graph of a function is shown below. based on the graph, what is the domain of this function? options: -3 ≤ x ≤ 1, -3 < x ≤ 1, 0 < x < -4, 0 ≤ x ≤ -4

Explanation:

Step1: Analyze the left endpoint

The left end of the graph has an open circle at \( x = -3 \), which means \( x = -3 \) is not included in the domain. So we use \( < \) for the left boundary.

Step2: Analyze the right endpoint

The right end of the graph has a closed circle at \( x = 1 \), which means \( x = 1 \) is included in the domain. So we use \( \leq \) for the right boundary.

Step3: Determine the domain

Combining the left and right boundaries, the domain of the function is \( -3 < x \leq 1 \).

Answer:

\( -3 < x \leq 1 \) (corresponding to the option: \( -3 < x \leq 1 \))