To create a T-chart for the function \( f(x) = 3(x+1) \) starting with \( x = 1 \) and \( x = 3 \), follow these steps:

### Step 1: Identify the function.
The given function is \( f(x) = 3(x+1) \).

### Step 2: Choose values for \( x \).
You have mentioned starting with \( x = 1 \) and \( x = 3 \), so I'll calculate \( f(x) \) for these values and include some additional values to create a complete T-chart.

### Step 3: Calculate \( f(x) \) for different values of \( x \).

\[
f(1) = 3(1 + 1) = 3(2) = 6
\]
\[
f(3) = 3(3 + 1) = 3(4) = 12
\]
Let's also calculate for \( x = 0 \), \( x = 2 \), and \( x = 4 \) to complete the chart:

\[
f(0) = 3(0 + 1) = 3(1) = 3
\]
\[
f(2) = 3(2 + 1) = 3(3) = 9
\]
\[
f(4) = 3(4 + 1) = 3(5) = 15
\]

### Step 4: Create the T-chart.

| \( x \) | \( f(x) = 3(x+1) \) |
|--------|---------------------|
| 1      | 6                   |
| 3      | 12                  |
| 0      | 3                   |
| 2      | 9                   |
| 4      | 15                  |

This is your T-chart for the function \( f(x) = 3(x+1) \) with the given values.

Would you like further details or have any questions?

### 5 Related Questions:
1. How would the chart change if the function were \( f(x) = 3x + 1 \) instead of \( 3(x+1) \)?
2. What does the slope of the linear function \( f(x) = 3(x+1) \) represent?
3. How do you graph the function \( f(x) = 3(x+1) \) based on the T-chart values?
4. How would adding a constant value to \( f(x) \) affect the T-chart?
5. What is the significance of intercepts in this function?

### Tip:
Always label the axes when plotting a graph from a T-chart to avoid confusion about which variable is represented.

Create a T-chart for the linear function f(x) = 3(x+1), starting with x=1 and x=3. This exercise covers key algebraic concepts, including function evaluation and T-chart construction. Suitable for students in Grades 6-8.

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