Answer:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex] (Since polinomial functions are continuous)
[tex]Ran\{f(x)\} = [-1, +\infty)[/tex] (As this quadratic function has an absolute minimum, represented by its vertex)
Step-by-step explanation:
Graphically speaking, quadratic functions are represented by parabolas. In this case, we have a parabola in factorized form. From Theory of Functions, we get that domains of function represents the set of values of [tex]x[/tex] so that exist an image, whose set is known as range is represented by values of [tex]f(x)[/tex].
[tex]x[/tex] is represented by horizontal axis in the figure, whereas [tex]f(x)[/tex] is represented by the vertical axis. By using this approach we get that domain and range of the function are, respectively:
[tex]Dom\{f(x)\} = \mathbb{R}[/tex] (Since polinomial functions are continuous)
[tex]Ran\{f(x)\} = [-1, +\infty)[/tex] (As this quadratic function has an absolute minimum, represented by its vertex)
