Supply a valid technology formula for the given function.
f(x) = 2x
f(x) =
Compute the missing values as indicated in the table below.
x	−3	−2	−1	0	1	2	3
f(x)

For the function \( f(x) = 2x \), the formula for \( f(x) \) is simply the equation \( f(x) = 2 \cdot x \). This means that for any input \( x \), the output \( f(x) \) is the value of \( x \) multiplied by 2.

Now, let's compute the missing values for each \( x \) in the table:

\[
f(x) = 2x
\]

For \( x = -3 \):  
\( f(-3) = 2 \cdot (-3) = -6 \)

For \( x = -2 \):  
\( f(-2) = 2 \cdot (-2) = -4 \)

For \( x = -1 \):  
\( f(-1) = 2 \cdot (-1) = -2 \)

For \( x = 0 \):  
\( f(0) = 2 \cdot 0 = 0 \)

For \( x = 1 \):  
\( f(1) = 2 \cdot 1 = 2 \)

For \( x = 2 \):  
\( f(2) = 2 \cdot 2 = 4 \)

For \( x = 3 \):  
\( f(3) = 2 \cdot 3 = 6 \)

The completed table is:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-3 & -6 \\
-2 & -4 \\
-1 & -2 \\
0 & 0 \\
1 & 2 \\
2 & 4 \\
3 & 6 \\
\hline
\end{array}
\]

Would you like a detailed explanation of how to interpret or use this function?

Here are five related questions:
1. What happens if you change the multiplier in \( f(x) = 2x \)?
2. How would the table look for \( f(x) = -2x \)?
3. Can you graph the function \( f(x) = 2x \) based on the table values?
4. What is the slope of the function \( f(x) = 2x \)?
5. How would you describe the relationship between \( x \) and \( f(x) \)?

**Tip:** When analyzing linear functions like \( f(x) = 2x \), the number multiplying \( x \) (in this case, 2) is called the slope, which determines how steep the line is.

Supply a valid technology formula for the given function. f(x) = 2x. Compute the missing values as indicated in the table below. x: -3, -2, -1, 0, 1, 2, 3

Learn how to compute the values of f(x) = 2x for x values ranging from -3 to 3. This exercise covers core algebraic concepts, specifically linear functions, suitable for students in Grades 6-8.

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