## College Algebra 7th Edition

domain: $(-\infty,\ \infty)$ range: $[4,\infty)$
We want to find the domain and range of: $F(t)=t^{2}+2t+5$ We factor the equation by completing the square: $t^{2}+2t+5$ $(t^{2}+2t+1)+5-1$ $(t+1)^{2}+4$ We can see that this is a shifted parabola ($t^2$ with the trough at x=-1, y=4 opening up). We know that F(t) will be larger than 4 for any $t$. Thus the range is: $[4,\infty)$. We also know that $x$ can be any real number, so the domain is: $(-\infty,\ \infty)$.