Question

What is the range of the fuction g(x)= |x - 12| -2

Answer 1

The range of this function is y = all real numbers such that y $\geq$ -2.

The way that you can tell the range of this function is by noting that inside the absolute value symbol can never be negative by the definition of an absolute value. So, we know that the smallest number that could come of that is 0. If the absolute value portion was equal to 0, then g(x) would be -2 due to the fact that you are subtracting 2. Since this is the smallest and there is no largest, we know that y is equal to all real numbers greater than or equal to -2.