Question

identify the domain of the function shown in the graph. a. $0leq xleq 8$ b. $-6leq xleq 6$ c. $x > 0$ d. $x$ is all real numbers.

Explanation:

Step1: Recall Domain Definition

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 (left - right) of the graph.

Step2: Analyze Each Option

• Option A: If the graph extends from \( x = 0 \) to \( x=8 \) (inclusive), then the domain is \( 0\leq x\leq8 \).
• Option B: \( - 6\leq x\leq6 \) would mean the graph is between \( x=-6 \) and \( x = 6 \), but if the graph's horizontal range is from 0 to 8, this is incorrect.
• Option C: \( x>0 \) implies the graph starts just to the right of \( x = 0 \) and goes to the right, but if the graph includes \( x = 0 \) and goes up to \( x = 8 \), this is incorrect.
• Option D: "x is all real numbers" would mean the graph extends infinitely in both the positive and negative \( x \)-directions, which is not the case here.

Assuming the graph of the function has a horizontal span from \( x = 0 \) (inclusive) to \( x=8 \) (inclusive), the domain is \( 0\leq x\leq8 \).

Answer:

A. \( 0\leq x\leq8 \)