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.

Answer 1

To transform the function \( f(x) = 3x \) to \( -f(3x-2) + 1 \), we follow these steps using proper order of operations (often remembered as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Start with the original function:
   \( f(x) = 3x \)

Now we will apply the transformations step-by-step to show how to get to \( -f(3x - 2) + 1 \).

Table Steps

| Step # | Expression | Operation | |---------|--------------------------------|--------------------------------| | 1 | \( 3x \) | Original function \( f(x) \) | | 2 | \( 3(3x - 2) \) | Substitute \( 3x-2 \) into \( f(x) \) | | 3 | \( 9x - 6 \) | Multiply \( 3 \times (3x - 2) \) | | 4 | \( -(9x - 6) + 1 \) | Apply the negative sign and add 1 | | 5 | \( -9x + 6 + 1 \) | Simplify to \( -9x + 7 \) |

Evaluating the Expressions

Now let's evaluate the expressions based on input \( x \):

Assume we are evaluating this transformation at \( x = 1 \).

1. Original: \[ 3(1) = 3 \]

2. Step 2: \[ 3(3(1) - 2) = 3(3 - 2) = 3(1) = 3 \]

3. Step 3: \[ 9(1) - 6 = 9 - 6 = 3 \]

4. Step 4: \[ -(9(1) - 6) + 1 = -(3) + 1 = -3 + 1 = -2 \]

5. Step 5: \[ -9(1) + 6 + 1 = -9 + 6 + 1 = -3 + 1 = -2 \]

Summary

The final evaluation would thus transform \( f(1) = 3 \) into \( -f(3(1)-2) + 1 = -2 \).

Please note, if you need to replace \( x \) with other values, you'll repeat similar computations for each value. If you indicate specific values for \( x \) for this table, I can help calculate those as well!