High School

The graph of a function \( f \) is shown below.

At which of the labeled \( x \)-values is the function least?

At which is it greatest?

Answer :

The least value of the function f occurs at point A, and the greatest value occurs at point D.

At point A, the function reaches its minimum value. This is evident because the graph is at its lowest point at this location, and no other point on the graph is lower.

Therefore, A represents the least value of the function.

Conversely, at point D, the function reaches its maximum value. This is clear because the graph is at its highest point at this location, and there are no other points on the graph that are higher.

Hence, D represents the greatest value of the function.

In summary, the least value of the function occurs at point A, and the greatest value occurs at point D based on the given graph.

These points correspond to the local minimum and maximum of the function, respectively, as indicated by the graph's shape and behavior.

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