To determine the domain of a graphed function, we need to identify the set of all possible input values (usually represented on the x-axis) for which the function is defined.
Since I do not have access to the image you're referring to, I'll guide you on how to assess the domain based on the graph you have.
-
Look for Gaps: Check if there are any values of \( x \) for which the function is not defined. For example, if there are vertical asymptotes or holes at certain \( x \)-values, these will not be included in the domain.
-
Assess Ranges: If the graph continuously extends without breaks, except for specific points, ensure you identify any excluded points carefully.
-
Check for Intervals: If the function appears to be defined for all real numbers except for certain values or within certain intervals, note those exclusions.
-
Consider the Ending of the Graph: If the graph continues indefinitely in both left and right directions without interruption, the domain might be all real numbers, \((-\infty, \infty)\).
Make sure to check these factors against your graph! If you find no interruptions and the graph appears continuous across all \( x \)-values, then the answer would be that the domain is all real numbers. If there are specific inputs that do not yield output, those values will need to be excluded from the domain.
Based on your choices, you could select "all Real numbers" if that's what your assessment indicates from the graph.