Question

The function f(x) = (x - 4)(x - 2) is shown below. What is true about the domain and range of the function?​

Answer 1

Answer:

$Dom\{f(x)\} = \mathbb{R}$ (Since polinomial functions are continuous)

$Ran\{f(x)\} = [-1, +\infty)$ (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 $x$ so that exist an image, whose set is known as range is represented by values of $f(x)$.

$x$ is represented by horizontal axis in the figure, whereas $f(x)$ is represented by the vertical axis. By using this approach we get that domain and range of the function are, respectively:

$Dom\{f(x)\} = \mathbb{R}$ (Since polinomial functions are continuous)

$Ran\{f(x)\} = [-1, +\infty)$ (As this quadratic function has an absolute minimum, represented by its vertex)