## Precalculus (6th Edition) Blitzer

The statement, “No quadratic functions have a range of $\left( -\infty ,\infty \right)$ ” is True.
The quadratic equation is defined as $f\left( x \right)=a{{x}^{2}}+bx+c$. Here, a, b, and c are constants and $a\ne 0$. The domain of the quadratic function is the set of real numbers because for each value of x in $f\left( x \right)=a{{x}^{2}}+bx+c,$ there exists the value of $f\left( x \right)$. If a is positive, the range of the quadratic function is the set of all positive real numbers. If a is negative, the range of the quadratic function is the set of all negative real numbers. Hence, for no values of a would the range of the function be the set of all real numbers. Therefore, the statement is true.