https://file.aiquickdraw.com/mathbot/file/17264182868890tefuike.jpg

The image you've uploaded contains a coordinate grid and a table of values that appears to represent points for a function \( f(x) \). The grid spans values from \(-5\) to \(5\) on both the \(x\)- and \(y\)-axes, and the table underneath lists values of \( x \) and corresponding \( f(x) \) values.

### The table values are:
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-5 & -5 \\
-4 & -4 \\
-3 & -3 \\
-2 & -2 \\
-1 & -1 \\
0 & 0 \\
1 & 1 \\
2 & 2 \\
3 & 3 \\
4 & 4 \\
5 & 5 \\
\hline
\end{array}
\]
This is likely a linear function of the form \( f(x) = x \), as for each value of \(x\), the value of \(f(x)\) is equal.

Would you like more details on this function or its graph? 

Here are 5 questions to deepen understanding:

1. How do we graph the points from this table on the coordinate plane?
2. What does the slope of the line \( f(x) = x \) represent?
3. How does this linear function behave as \( x \to \infty \)?
4. Can we generalize this function to one with a different slope, such as \( f(x) = 2x \)?
5. What is the significance of the line \( f(x) = x \) in geometry?

**Tip:** For linear functions, the slope is the key feature that determines how steep the line is!

Create a table of values and plot the linear function f(x) = x on a coordinate grid.

Learn how to graph the linear function f(x) = x using a table of values and plot it on a coordinate grid. This example covers the basic concepts of linear functions and their graphical representation, suitable for students in Grades 6-8.

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