Question

1. a part of a linear function is shown on the grid.

what is the range of the part of the linear function shown?
choose the correct answer from each drop - down menu to complete the sentence.
the range is the set of all real numbers -- choose the correct answer -- and -- choose the correct answer --.

Explanation:

Step1: Identify the y - values of the endpoints

The solid dot is at $(-2, 2)$ and the open dot is at $(3, - 4)$. The open dot means the point is not included, and the solid dot means the point is included.

Step2: Determine the range

For a linear function (a line segment here), the range is the set of all y - values between the minimum and maximum y - values of the segment. The maximum y - value is 2 (from the solid dot, so included) and the minimum y - value is - 4 (from the open dot, so not included). So the range is all real numbers greater than - 4 and less than or equal to 2 (or we can say from - 4 (not included) to 2 (included)).

Answer:

The range is the set of all real numbers greater than - 4 and less than or equal to 2 (or in the form: The range is the set of all real numbers \(\boldsymbol{> - 4}\) and \(\boldsymbol{\leq 2}\)).