Question

write a piecewise function defined by three equations that has a domain of all real numbers and a range of "-3

Answer 1

A piece-wise function that has domain of all real numbers and range of $[-3, \infty)$ is f(x) = |x| - 3, as:

$|x| - 3 = x - 3, x \geq 0$

$|x| - 3 = -x - 3, x < 0$

What is a piece-wise function?

A piece-wise function is a function that has different definitions, depending on the input.

One example is the absolute value function, defined as follows:

$|x| = x, x \geq 0$

$|x| = -x, x < 0$

The function is defined for all real values, with a range of $[0, \infty)$. Shifting it down 3 units, it will have the desired range, as follows:

$|x| - 3 = x - 3, x \geq 0$

$|x| - 3 = -x - 3, x < 0$

More can be learned about piece-wise functions at brainly.com/question/27262465

#SPJ1