# How do you find the domain and range for F(x) = 6x^2 - 2x +7?

May 27, 2015

Domain is $\mathbb{R}$, range is <6 5/6;+oo)

This function is a polynomial, so its domain is whole set $\mathbb{R}$.

To find the range you have to see, that the coefficient next to ${x}^{2}$ is positive, so the graph is going to $+ \infty$ as the argument $x$ goes to $- \infty$ or $+ \infty$, so the range can be written as
< q;+oo) where $q = f \left(p\right)$ and $p = - \frac{b}{2 a}$

$p = \frac{2}{12} = \frac{1}{6}$
$q = f \left(\frac{1}{6}\right) = 6 \cdot {\left(\frac{1}{6}\right)}^{2} - 2 \cdot \frac{1}{6} + 7 = \frac{1}{6} - \frac{2}{6} + 7 = - \frac{1}{6} + 7 = 6 \frac{5}{6}$