### Instruction: Compute the range of the function $f(x) = \sqrt{x^2}$.### Response: The range of a function is the set of possible outputs or y-values that the function can produce.
To find the range, I need to think about what values can x take, and what values can the square root of x squared take.
I know that x can be any real number, so x can be positive, negative, or zero.
I also know that the square root of a number is always non-negative, meaning zero or positive.
That means that the square root of x squared can never be negative, even if x is negative.
For example, if x is -2, then the square root of x squared is the square root of (-2)^2, which is the square root of 4, which is 2.
So, for any x, the square root of x squared is either zero or a positive number.
This means that the range of f(x) is the set of all non-negative real numbers.
I can write this using interval notation as [0, infinity).