Question

If an absolute value function has a minimum of (−3,4) and another has a maximum at (−3,4), how do their ranges compare? Explain.

A) They have the same range due to the identical coordinates.
B) Their ranges differ because of the opposite function behaviors.
C) Both ranges vary since they have different extrema.
D) Ranges are undefined without additional information.

Answer 1

Absolute value functions with a minimum at a specific point and functions with a maximum at the same point have different ranges due to their opposing behaviors. The correct answer is B).

Step-by-step explanation:

If an absolute value function has a minimum of −3,4) and another function has a maximum at (−3,4), then their ranges differ. The term 'range' in mathematics refers to the set of all possible output values, which depends on the overall behavior of the function.

An absolute value function with a minimum suggests it is an upright "V" shape, indicating that the range starts at the minimum point and extends upwards infinitely. Conversely, a function with a maximum at the same point implies that the range is bounded above by that maximum and extends downwards.

In conclusion, the correct answer is B) Their ranges differ because of the opposite function behaviors. Without additional information on the specific behavior past the single point provided, we cannot determine the exact range of either function.