Answer:
(-2, 10].
Explanation:
First of all, let's refresh the concepts of domain and range when talking about mathematical functions.
In simple terms, the domain of a function are the values that the function can work with, the allowed inputs, which happen to be the same as values of the common used variable "x", the dependent variable. We can easily tell the domain of a by looking at its horizontal extension, what values of "x" it passes by.
Now, the domain is the total opposite, those are the outputs, or the "y" values that the function returns after evualiating an "x" value. These can be seen by analyzing the vertical extension of the graph, what values of "y" the function can reach.
In the given graph, we may see that the lowest "y" value the graph outputs (vertically) is -2, and we also see that the circle in that number doesn't have a fill color, it's transparent, that means that tne function doesn't contain the value of -2. Therefore, y > -2. Now, on the upper end of the function, we can see that highest "y" value the function can reach is 10, marked with a filled circle, which means that the function contains said value, hence, y ≤ 10.
Now, writting in interval notation, remember that the square brackets "[]" are meant to be used next to a value that the function contains. Also, the parentheses "()" are meant to a value that the function doesn't contain.
Previously, we mentioned that the function doesn't contain value "-2", therefore, we may write:
(-2...
Now, to finish writting the interval, we mentiones that value 10 is contained in the function, hence, we finish writting the interval notation as follows:
(-2, 10].
Final answer: (-2, 10].
Check the attached image to better understand the interval notation.
Important note.
When writting in interval notaion, the symbol of infinity "∞" must always be written next to a parenthesis symbol.