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Question
What is the domain of the graphed function?
Responses
A y ≥ 4y ≥ 4
B x ≥ -2x ≥ -2
C y ≥ -2y ≥ -2
D x ≤ -2x ≤ -2
E all real numbers
The domain of a graphed function is the set of all possible x-values for which the function is defined. From the given graph, it can be seen that the function is defined for all x-values. Therefore, the domain of the graphed function is "all real numbers". Therefore, the correct answer is E.
To determine the domain of a graphed function, we need to look at the x-values for which the graph exists.
In this case, the graph appears to have a shaded region on the left side of the y-axis. This implies that the function is defined for x-values less than or equal to a certain value.
Looking at the answer choices:
A) y ≥ 4: This choice relates to the range (or y-values) of the function, not the domain (or x-values).
B) x ≥ -2: This choice is not relevant to the given graph. The shaded region is to the left of the y-axis, not the right.
C) y ≥ -2: This choice also relates to the range (or y-values) of the function, not the domain (or x-values).
D) x ≤ -2: This choice correctly describes the domain of the function. The shaded region indicates that the function is defined for x-values less than or equal to -2.
E) All real numbers: This choice is too broad and not supported by the graph.
Therefore, the correct answer is D) x ≤ -2, which represents the domain of the graphed function.