Question

consider the function represented by the graph.
graph of a line from (0,9) to (8,1)
what is the domain of this function?
{ x | x ≥ 0 }
{ x | x ≤ 0, x ≥ 8 }
{ x | x ≤ 8 }
{ x | 0 ≤ x ≤ 8 }

Explanation:

Step1: Understand Domain

The domain of a function is the set of all possible \( x \)-values (input values) for which the function is defined. For a graph, we look at the horizontal extent of the graph (left to right).

Step2: Analyze the Graph

Looking at the graph, the line starts at \( x = 0 \) (the \( y \)-intercept is at \( (0, 9) \)) and ends (or extends to) \( x = 8 \) (the arrow is at \( x = 8 \) on the right). So the \( x \)-values range from \( 0 \) to \( 8 \), including both endpoints.

Step3: Match with Options

• The first option \( \{x | x \geq 0\} \) is incorrect because the graph doesn't go beyond \( x = 8 \) to the right.
• The second option \( \{x | x \leq 0, x \geq 8\} \) is incorrect as the graph is between \( 0 \) and \( 8 \), not outside.
• The third option \( \{x | x \leq 8\} \) is incorrect because the graph doesn't include \( x < 0 \) (it starts at \( x = 0 \)).
• The fourth option \( \{x | 0 \leq x \leq 8\} \) correctly represents the \( x \)-values from \( 0 \) to \( 8 \), inclusive.

Answer:

\(\{x | 0 \leq x \leq 8\}\)