Graph the function represented by the table below. Is the function linear or​ nonlinear?

Question

x
0
1
2
3
4
y
0
4
8
12
16
Question content area bottom left
Part 1
Graph the function.
.
.
.
Question content area bottom right
Part 1
Choose the correct graph below.
A.
-1
5
-8
20
x
y

x y graph
B.
-8
20
-1
5
x
y

x y graph
C.
-8
20
-1
5
x
y

x y graph
D.

Answer 1

To determine whether the function represented by the table is linear or nonlinear, we first need to analyze the values in the table:

\[ \begin{array}{|c|c|} \hline x & y \ \hline 0 & 0 \ 1 & 4 \ 2 & 8 \ 3 & 12 \ 4 & 16 \ \hline \end{array} \]

Next, we can observe the change in \(y\) as \(x\) increases by 1:

• From \(x = 0\) to \(x = 1\), \(y\) changes from 0 to 4 (increases by 4).
• From \(x = 1\) to \(x = 2\), \(y\) goes from 4 to 8 (increases by 4).
• From \(x = 2\) to \(x = 3\), \(y\) goes from 8 to 12 (increases by 4).
• From \(x = 3\) to \(x = 4\), \(y\) goes from 12 to 16 (increases by 4).

Since the change in \(y\) is consistent (always increases by 4), this indicates that the function is linear.

Graphing the Function

To graph this function, plot the points \((0,0)\), \((1,4)\), \((2,8)\), \((3,12)\), and \((4,16)\) on a coordinate plane. Connect the points with a straight line, as this confirms the linearity visually.

Identifying the Correct Graph

Since you provided options A, B, C, and D but didn't include their visuals, you would need to select the graph that shows a straight line passing through those points. A graph that is linear will appear as a straight line.

If you can see the options and one of them is a straight line through the points mentioned, that would be the correct choice. If the graph has any curves or does not connect these points with a straight line, then it is not the correct representation of the function.

Please choose the graph that aligns with this description. If you provide more details about the graphs, I can help you further in identifying which one is the correct representation.