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Domain and range:

The domain of a function is all the values the the input assumes.

The range of a function is given by all the values that the output assumes.

In a graphic:

The domain is given by the x-values, the horizontal axis.

The range is given by the y-values, the vertical axis.

In this question:

x, in the horizontal axis, assumes values between -4 and 2.

The closed circle at x = -4 and x = 2 indicates that these values are part of the interval.

Thus, the domain of the graphed function is: [tex]-4 \leq x \leq 2[/tex], and the correct answer is given by option D.

For more about domain and range of functions, you can check: https://brainly.com/question/21853810?referrer=searchResults

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D. [tex]-4 \le x \le 2[/tex]

The procedure of solution consist consist in determine graphically the Domain of the Function shown in the figure. In this case, the Domain is the Set of values of [tex]x[/tex] in Interval notation, which represented in the "horizontal" axis of the Cartesian Plane. Please notice that black points means that given Function includes extreme values.

By visual examination of the function, we conclude that domain of the function is represented by:

[tex]Dom\{f(x)\} = [-4, 2][/tex]

Which is equivalent to the following expression in Inequality notation:

[tex]-4 \le x \le 2[/tex]

Therefore, we conclude that right answer is D.

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