Question

Correctly show the order of operations that transforms f (x)
Complete the table.
==
3 to f(3x-2)+ 1.
You should write the new function first to help you fill out the table.
In the table in row 1, you should put the expression used to find the value of x in the correct order of operations. Progress
by rewriting the expression in each subsequent step, applying an additional operation one at a time, until all 5 steps are
complete.
In rows 2-4, you will put the number you find after evaluating the expression for the value of x.
Drag the steps into the chart
(5 points)
In the order of
operations, what
would you do first?
x
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Options are:
3x - 2
3x
3^(3x-2)
-3^(3x-2)
3x3^x
-(3x-2)+1
-3x+3
(-3x+2)+1
3
3x-1
-3^(3x-2) + 1

Answer 1

only one choice option per step no repeats

Answer 2

what's step 5 after -3(^3x-2)+1

Answer 3

To transform \( f(x) \) based on the expression \( f(3x - 2) + 1 \), we want to apply the order of operations in a step-by-step manner. Let’s label this transformation and break it down accordingly.

Starting with the expression \( 3x - 2 \):

1. **Step 1**: We start with the expression \( 3x - 2 \).
2. **Step 2**: We evaluate \( 3x - 2 \) first.
3. **Step 3**: Then, we apply \( 3^{(3x - 2)} \).
4. **Step 4**: Now, we apply the negative, \( -3^{(3x - 2)} \).
5. **Step 5**: Finally, we add 1, resulting in \( -3^{(3x - 2)} + 1 \).

Now, let's fill in the table with these computations:

| Step | Expression | Result |
|-------|-----------------------------------------------------|---------------|
| Step 1| Start with \( 3x - 2 \) | - |
| Step 2| Evaluate \( 3x - 2 \) | \( 3x - 2 \) |
| Step 3| Calculate \( 3^{(3x - 2)} \) | \( 3^{(3x - 2)} \) |
| Step 4| Apply negative: \( -3^{(3x - 2)} \) | \( -3^{(3x - 2)} \) |
| Step 5| Final step: \( -3^{(3x - 2)} + 1 \) | \( -3^{(3x - 2)} + 1 \) |

Now, let's put in the values:

1. For \( x = 1 \):
- Step 1: \( 3(1) - 2 = 1 \)
- Step 2: \( 3^{1} = 3 \)
- Step 3: \( -3 = -3 \)
- Step 4: \( -3 + 1 = -2 \)

2. For \( x = 2 \):
- Step 1: \( 3(2) - 2 = 4 \)
- Step 2: \( 3^{4} = 81 \)
- Step 3: \( -81 = -81 \)
- Step 4: \( -81 + 1 = -80 \)

3. For \( x = 3 \):
- Step 1: \( 3(3) - 2 = 7 \)
- Step 2: \( 3^{7} = 2187 \)
- Step 3: \( -2187 = -2187 \)
- Step 4: \( -2187 + 1 = -2186 \)

Make sure to verify each computation at each step to ensure accuracy based on the transformation of the function.

Answer 4

Got it! Let's revise the steps following the order of operations more clearly with only one choice option per step without repetition. We will use the initial expression \( f(3x - 2) + 1 \) and only perform one operation at a time.

### Complete Table of Steps:

| Step | Expression | Result |
|-------|----------------------------------------------------|----------------|
| Step 1| Start with \( 3x - 2 \) | \( 3x - 2 \) |
| Step 2| Evaluate \( 3x \) | \( 3x \) |
| Step 3| Calculate \( 3x - 2 \) | \( 3x - 2 \) |
| Step 4| Calculate \( 3^{(3x - 2)} \) | \( 3^{(3x - 2)} \) |
| Step 5| Final operation: \( -3^{(3x - 2)} + 1 \) | \( -3^{(3x - 2)} + 1 \) |

### Values for Each Step:

1. For \( x = 1 \):
- Step 1: \( 3(1) - 2 = 1 \)
- Step 2: \( 3^{(3 \cdot 1 - 2)} = 3^1 = 3 \)
- Step 3: \( -3^{(3 \cdot 1 - 2)} + 1 = -3 + 1 = -2 \)

2. For \( x = 2 \):
- Step 1: \( 3(2) - 2 = 4 \)
- Step 2: \( 3^{4} = 81 \)
- Step 3: \( -3^{4} + 1 = -81 + 1 = -80 \)

3. For \( x = 3 \):
- Step 1: \( 3(3) - 2 = 7 \)
- Step 2: \( 3^{7} = 2187 \)
- Step 3: \( -3^{7} + 1 = -2187 + 1 = -2186 \)

Please confirm if this satisfies your requirements regarding the operations, and if you need any more adjustments!

Answer 5

Let's clarify the simplification in Step 5 after we reach the expression \(-3^{(3x - 2)} + 1\).

### Expression Breakdown
1. **Start with: \(-3^{(3x - 2)} + 1\)**

### Evaluating Step 5
- You would evaluate the expression \( -3^{(3x - 2)} + 1 \) based on what you have derived from the previous steps.

### Example with \( x = 1 \)
- If \( x = 1 \):
- Calculate \( 3(1) - 2 = 1 \)
- Now \( -3^{(3(1) - 2)} + 1 = -3^1 + 1 = -3 + 1 = -2 \)

### Example with \( x = 2 \)
- If \( x = 2 \):
- Calculate \( 3(2) - 2 = 4 \)
- Now \( -3^{(3(2) - 2)} + 1 = -3^4 + 1 = -81 + 1 = -80 \)

### Example with \( x = 3 \)
- If \( x = 3 \):
- Calculate \( 3(3) - 2 = 7 \)
- Now \( -3^{(3(3) - 2)} + 1 = -3^7 + 1 = -2187 + 1 = -2186 \)

### Final Summary of Step 5
Thus, Step 5 calculates the final output of the function by plugging in the value of \( x \) appropriately into the expression you've derived:

- For \( x = 1 \): Result is **-2**
- For \( x = 2 \): Result is **-80**
- For \( x = 3 \): Result is **-2186**

**Final output for Step 5**: Result of \( -3^{(3x - 2)} + 1 \) based on the evaluated \( x \).