consider the data set shown on the graph.\nwhat point should be removed from the data set to have the graph…

Explanation:

Step1: Recall function definition

A function requires each input ($x$-value) to map to exactly one output ($y$-value).

Step2: Identify duplicate x-values

Check all points: $(-5,-4), (-4,-1), (-3,4), (-1,-1), (0,2), (0,-2), (1,1), (2,-1), (3,3), (4,0), (4,-2)$. The $x$-value $x=0$ has two $y$-values: $2$ and $-2$; $x=4$ has two $y$-values: $0$ and $-2$.

Step3: Select removable point

Either $(0,-2)$ or $(0,2)$, or $(4,0)$ or $(4,-2)$ can be removed. The most straightforward choice is one of the duplicate pairs, e.g., $(0,-2)$.

Answer:

$(0,-2)$ Note: $(0,2)$, $(4,0)$, or $(4,-2)$ are also valid correct answers.