Use a table of values to graph the following functions. State the domain and range.

$\mathit{y}\mathbf{=}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{x}\mathbf{+}\mathbf{5}$

The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible $x$-values that will make the function "work" and will output real $y$-values.

Therangeof a function is the complete set of all possibleresulting valuesof the dependent variable ($y$,usually) after we have substituted the domain.

For the equation,$y=x^2+2x+5$,make a table to get some points on the graph.

Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.

Graph the ordered pairs, and connect them to create a smooth curve. The parabola extends to infinity.

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value or $\left\{y|y\ge 4\right\}$.