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.