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

Question

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

GPT-4o mini · Answer

To transform the function $ f(x) = 3x $ into $ -f(3x-2) + 1 $, we will follow the steps required to manipulate the expression step by step. Let's analyze how to perform the transformations: 1. Start with $ f(x) = 3x $. 2. Substitute $ 3x-2 $ into the function: $ f(3x-2) = 3(3x-2) $. 3. Evaluate that expression: $ 3(3x-2) = 9x - 6 $. 4. Apply the negative sign: $ -f(3x-2) = -(9x - 6) = -9x + 6 $. 5. Finally, add 1 to the result: $ -9x + 6 + 1 = -9x + 7 $. Now, we can fill out the table: --- ### Transformation Steps Table | Step | Expression | Value for $ x $ | |------|-------------------------------------------------|-------------------| | 1 | $ f(x) = 3x $ | | | 2 | $ f(3x - 2) = 3(3x-2) $ | | | 3 | $ 3(3x - 2) = 9x - 6 $ | | | 4 | $ -f(3x - 2) = -(9x - 6) = -9x + 6 $ | | | 5 | $ -9x + 6 + 1 = -9x + 7 $ | | --- Next, let’s input a particular value for $ x $ to evaluate the function at different steps: Let's say we evaluate $ x = 1 $: 1. For $ f(1) $, we calculate $ f(1) = 3(1) = 3 $. 2. Substitute $ x = 1 $: Compute $ f(3(1)-2) = f(3-2) = f(1) = 3 $. 3. At that point, $ 3(1-2) = 3(1) - 6 = 9 - 6 = 3 $. 4. Calculate $ -f(1) = -3 $. 5. Finally: $ -3 + 1 = -2 $. Inputting the calculated values based on $ x = 1 $: - **Row 1:** $ 3 $ - **Row 2:** $ 3 $ - **Row 3:** $ 3 $ - **Row 4:** $ -3 $ - **Row 5:** $ -2 $ --- ### Final Values | x | In the order of operations, what would you do first? | |----|--------------------------------------------| | 1 | $ 3(1) = 3 $ | | 2 | $ 3(3(1) - 2) = 3(1) = 3 $ | | 3 | $ 3(3(1) - 6) = 3(9 - 6) = 3 $ | | 4 | $ -3 $ | | 5 | $ -3 + 1 = -2 $ | Feel free to change $ x $ to any desired value to get different evaluations!