Question

the graph of the function f(x) = -2x - 2 is shown. which set - builder notation represents the domain of the function in the graph? options: {x | -6 ≤ x ≤ -2}, {x | -3 ≤ x ≤ 2}, {y | -6 ≤ y ≤ 4}

Explanation:

Step1: Identify the domain's definition

The domain of a function is the set of all possible \( x \)-values (input values) for the function. So we need to find the range of \( x \)-values covered by the graph.

Step2: Analyze the graph's \( x \)-intercepts

Looking at the graph, we can see the leftmost point (minimum \( x \)-value) and the rightmost point (maximum \( x \)-value). From the graph, the leftmost \( x \)-value is \( -3 \) and the rightmost \( x \)-value is \( 2 \). So the domain is all \( x \) such that \( -3 \leq x \leq 2 \).

Step3: Eliminate incorrect options

• Option 1: \( \{x|-6\leq x\leq -2\} \) is incorrect as the \( x \)-range in the graph is from -3 to 2, not -6 to -2.
• Option 3: \( \{y|-6\leq y\leq 4\} \) is incorrect because it represents the range (set of \( y \)-values), not the domain (set of \( x \)-values).

Answer:

\(\{x|-3\leq x\leq 2\}\) (assuming the middle option is this one, as per the analysis)