Correctly show the order of operations that transforms f(x) = 3x

Question

to −f(3x−2)+1
.

Complete the table.

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)
Drop target 1
Drop target 2
Drop target 3
Drop target 4
Drop target 5
Question 2
Correctly show the order of operations that transforms f(x) = 3x
to −f(3x−2)+1
.

Complete the table.

In rows 2-4, you will put the number you find after evaluating the expression for the value of x.

(8 points)
x
In the order of operations, what would you do first?

STEP 1:

STEP 2: STEP 3: STEP 4: STEP 5:
1
2
3

Answer 1

To transform \( f(x) = 3x \) to \( -f(3x - 2) + 1 \), you'll need to follow a series of steps according to the order of operations. Let's break down the transformation step by step.

1. Original function: \( f(x) = 3x \)
2. Evaluate: \( f(3x - 2) = 3(3x - 2) \)
3. Apply the negative: \( -f(3x - 2) = -3(3x - 2) \)
4. Simplify: \( -3(3x - 2) + 1 = -9x + 6 + 1 \)
5. Final function: \( -9x + 7 \)

Now, let's fill in the order of operations in the table:

Table: Steps for Transformation

| Step | Expression | Value | |----------|-------------------------|------------------| | STEP 1 | \( 3x - 2 \) | \( 3x - 2 \) | | STEP 2 | \( f(3x - 2) = 3(3x - 2) \) | \( 3(3x - 2) = 9x - 6 \) | | STEP 3 | \( -f(3x - 2) \) | \( -(9x - 6) = -9x + 6 \) | | STEP 4 | \( -f(3x - 2) + 1 \) | \( -9x + 6 + 1 = -9x + 7 \) | | STEP 5 | Final Function | \( -9x + 7 \) |

In the order of operations, what would you do first?

Fill in the "In the order of operations" column:

1. Evaluate \( 3x - 2 \)
2. Substitute \( 9x - 6 \) from \( f(3x - 2) \)
3. Apply negative sign: \( -9x + 6 \)
4. Add 1: \( -9x + 7 \)
5. Final function: \( -9x + 7 \)

For evaluating \( -f(3x - 2) + 1 \), you can plug in different values for \( x \) as required.

If there is a specific value of \( x \) you want to evaluate or if you have additional parameters, please let me know!