Zeke claims that the function to the left should have three shaded regions for its range because it is a three-piece piecewise function. Is Zeke correct? Yes or No

The function on the left of the graph should have two shaded regions for its range because the range of the two functions overlaps. Therefore, no the claim of Zeke is incorrect.

Given :

The graph shows the piece-wise function.

The following steps can be used to determine that the Zeke claims is correct or not:

Step 1 - The domain of the graph of the function present in the third and fourth quadrant is:      

Step 2 - The domain of the graph of the function present in the second quadrant is:

Step 3 - The domain of the graph of the function present in the first quadrant is:

The function on the left of the graph should have two shaded regions for its range because the range of the two functions overlaps. Therefore, no the claim of Zeke is incorrect.

For more information, refer to the link given below:

link

No

Step-by-step explanation:

The input to a function which is the domain of the function is the x-variable or independent variable, while the output of a function which is the range of the function is the y-variable or dependent variable

In the given function, the outputs or the ranges of the function for the input of piece with x-values -3 ≤ x ≤ -8 completely overlaps the ranges for the piece with x-values 1 < x ≤ 3, therefore, both ranges can be represented by a single shaded region, giving a total of two shaded regions.