Correctly show the order of operations that transforms f(x)=3^x to -f(3x-2)+1 first write the new function

Question

In the table in row 1 put the expression used to find the value of x in the correct order of operations continue rewriting the expression in each subsequent step apply an additional operation one at a time until all 5 steps are complete
In rows 2-4 put the number you find after evaluating the expression forage value of x
Here are the options
3^(3x-2)
-3x+3
3
3x
3x-2
-3^(3x-2) +1
3x-1
-(3x-2)+1
3*3^x
(-3x+2)+1
-3^(3x-2)

Answer 1

To transform the function \( f(x) = 3^x \) into the new function \( -f(3x-2) + 1 \), we can represent the steps we would take in this transformation. The operation is essentially the following:

1. Start with \( f(x) = 3^x \).
2. Substitute \( 3x - 2 \) into the function: \( f(3x - 2) = 3^{(3x - 2)} \).
3. Apply the negative sign: \( -f(3x - 2) = -3^{(3x - 2)} \).
4. Add 1: \( -3^{(3x - 2)} + 1 \).

Now, for your table, we'll fill it out step-by-step using the expressions provided, based on the order of operations we performed.

New Function:

\[ -f(3x-2) + 1 \]

Table:

| Step | Expression | Result (for a chosen value of x, e.g., \( x = 1 \)) | |------|------------|------------------------------------------------| | 1 | \(3^{(3x-2)}\) | \(3^{(3(1)-2)} = 3^{1} = 3\) | | 2 | \(-3^{(3x-2)}\) | \(-3^{(3(1)-2)} = -3^{(1)} = -3\) | | 3 | \(-3^{(3x-2)} + 1\) | \(-3 + 1 = -2\) |

Completed Table:

| Step | Expression | Result | |------|-----------------------------|--------| | 1 | \(3^{(3x-2)}\) | 3 | | 2 | \(-3^{(3x-2)}\) | -3 | | 3 | \(-3^{(3x-2)} + 1\) | -2 |

Note: The values in the "Result" column are specifically for \( x = 1 \). You can substitute any other value of \( x \) into the expressions to find different results.