Q. 103 - Precalculus Enhanced with Graphing Utilities

Question

Can a quadratic function have a range of $(-\infty ,\infty )$ ? Justify your answer.

Step-by-Step Solution

Answer

No there does not exist a quadratic function whose range is of whole real numbers

Step 1: Given information

We are asked that is there a function $f\left(x\right)=a{x}^2+bx+c$ whose range is $(-\infty ,\infty )$

Step 2: Explanation

No. there does not exist a quadratic equation whose range is whole real numbers. It is not possible for a function to have range of whole real numbers There must be a minimum and maximum value that will be located at the functions vertex.