Given the function $f(x) = x - 1$, we are asked to find the table that represents $g(x) = 3 \cdot f(x)$.

Step 1: Express $g(x)$ using $f(x)$

Since $f(x) = x - 1$, we can express $g(x)$ as:

$g(x) = 3 \cdot f(x) = 3 \cdot (x - 1) = 3x - 3$

Step 2: Compute values for $g(x)$

We will use various values of $x$ to calculate $g(x)$.

• For $x = 1$: $g(1) = 3(1) - 3 = 3 - 3 = 0$

• For $x = 2$: $g(2) = 3(2) - 3 = 6 - 3 = 3$

• For $x = 3$: $g(3) = 3(3) - 3 = 9 - 3 = 6$

• For $x = 4$: $g(4) = 3(4) - 3 = 12 - 3 = 9$

• For $x = 5$: $g(5) = 3(5) - 3 = 15 - 3 = 12$

Step 3: Construct the table for $g(x)$

$x$	$f(x) = x - 1$	$g(x) = 3x - 3$
1	0	0
2	1	3
3	2	6
4	3	9
5	4	12

This table shows the values of both $f(x)$ and $g(x)$.

Would you like more details on this process or have any questions?

Related Questions:

1. How do transformations of functions work, such as multiplying by a constant?
2. What does the graph of $g(x) = 3x - 3$ look like compared to $f(x) = x - 1$?
3. How would we calculate the inverse of $g(x)$?
4. What effect does changing the coefficient (3 in this case) have on the graph of a linear function?
5. How can you test if a transformation has been applied correctly to a function?

Tip:

When scaling a function by a constant (like multiplying by 3), it stretches the graph vertically if the constant is greater than 1 or compresses it if it’s between 0 and 1.