Question

consider the function represented by the graph. what is the domain of this function? options: {x|x ≥ 0}, {x|x ≤ 8}, {x|0 ≤ x ≤ 8}, {x|x ≤ 0 x ≥ 8}

Explanation:

Step1: Recall domain definition

Domain is the set of all x - values for which the function is defined (the x - values covered by the graph).

Step2: Analyze the graph's x - values

The graph starts at \(x = 0\) (the y - intercept point \((0,9)\)) and ends at \(x=8\) (the endpoint \((8,1)\)). So the x - values of the function range from \(0\) to \(8\), inclusive. This means the domain is all real numbers \(x\) such that \(0\leq x\leq8\), or in set - builder notation \(\{x|0\leq x\leq8\}\).

Answer:

\(\{x|0\leq x\leq8\}\) (the third option)