Question

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