Question

What is the range of the function f(x) = |x − 1| − 2?all real numbersall real numbers less than or equal to −2all real numbers less than or equal to 1all real numbers greater than or equal to −2?

Answer 1

The range of the function f(x) = |x - 1| - 2 is all real numbers greater than or equal to -2.

Step-by-step explanation:

The function f(x) = |x - 1| - 2 represents the absolute value of x minus 1, subtracted by 2.

The range of the function can be determined by finding the minimum and maximum values it can take.

Since the absolute value of a number is always greater than or equal to zero, the lowest value that f(x) can take is when |x - 1| = 0, which happens when x = 1.

Therefore, the minimum value of f(x) is -2.

As x increases or decreases from 1, the value of f(x) increases.

So, there is no upper bound for the range of f(x).

Therefore, the range of the function is all real numbers greater than or equal to -2.

Answer 2

The minimum value of the function is -2, so the range is
.. all real numbers greater than or equal to -2 . . . . the last selection