# What is the range of the function 2(x-3)^2+1?

Jan 12, 2018

Range: $f \left(x\right) \in \left[1 , + \infty\right)$
Note that ${\left(x - 3\right)}^{2}$ has a minimum value of $\textcolor{b l u e}{0}$
in which case $2 {\left(x - 3\right)}^{2} + 1$ has a value of $\textcolor{red}{1}$
Also note that ${\left(x - 3\right)}^{2}$ has no upper limit
so as the value of ${\left(x - 3\right)}^{2}$ increases $2 {\left(x - 3\right)}^{2} + 1 \rightarrow + \infty$