Question

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

Short answer

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

Step-by-step solution

Given information

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

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.