Question

Create a function with a domain of all real numbers and the range all real numbers that are greater than or equal to zero. Provide the function both graphically and in function notation

Answer 1

Explanation:

Any polynomial function has the domain of all real numbers. So here we'll choose a polynomial function in order to illustrate this problem. So any polynomial of the form:

$f(x)=a(x+h)^n \\ \\ \\ For: \\ \\ a>0 \\ \\ n \ even \\ \\ h \ any \ constant$

meets our requirements. Therefore, if we set:

$a=1 \\ \\ n=2 \\ \\ h=3$

Then, we'll have:

• A domain of all real numbers and the range all real numbers that are greater than or equal to zero.

This is shown graphically in the figure below.