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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:3x
-3(3x-2)
3 x 32
-(3x-2)+1
-3x+3
(-3x+2)+1
3
3x-2
3(3x-2)
3x-1
-3(3x-2)+1

3 answers

To transform the function \( f(x) \) to \( f(3x-2) + 1 \) and complete the table, we start with the expression \( 3x - 2 \) and apply the operations in the correct order.

Function Transformation

We are transforming: \[ f(x) \quad \text{to} \quad f(3x-2) + 1 \]

Order of Operations Steps

Let's break down how we can evaluate this expression step by step:

  1. Step 1: Plug in \( x \) into the function expression.

    • Expression: \( 3(3x - 2) + 1 \)

  2. Step 2: Distribute the 3.

    • Expression: \( 9x - 6 + 1 \)

  3. Step 3: Combine like terms (add -6 and 1).

    • Expression: \( 9x - 5 \)

  4. Step 4: Now we have \( f(3x - 2) + 1 \) evaluated to \( 9x - 5 \).

    • Expression: Resulting function is \( 9x - 5 \)

  5. Step 5: Final form of the function (if needed for a specific value).

    • Expression could evaluate at a specific x-value if necessary.

Filling in the Table

| Step | Expression | Result | |--------|-----------------------------------|-----------| | Step 1 | \( 3(3x - 2) + 1 \) | | | Step 2 | \( 9x - 6 + 1 \) | | | Step 3 | \( 9x - 5 \) | | | Step 4 | (Function transformation complete) | | | Step 5 | (Final result, if applicable) | |

Applying given options to find results

Now, let's evaluate the actual numerical values. If we want specific results, we'd plug in a value for \( x \) -- for example, if \( x = 1 \):

  1. \( 3(3(1) - 2) + 1 \) would become:
    • \( 3(3 - 2) + 1 \) = \( 3(1) + 1 \) = 3 + 1 = 4.

So:

  • Step 1 Expression: \( 3(3x-2) + 1 \)
  • Result for \( x = 1 \): \( 4 \)

You can apply any value you choose for \( x \) in this manner. For the remaining table cells, you can derive results based on whatever values you wish to use for \( x \).

Please let me know if you need more specific values or any other assistance!

keep in mind that it is 3^(3x-2) and then + 1

Thank you for the clarification! Given that the expression is \( 3^{(3x - 2)} + 1\), let’s rewrite the transformation and fill in the table accordingly.

Function Transformation

We are transforming: \[ f(x) \quad \text{to} \quad f(3x - 2) + 1 \Rightarrow 3^{(3x - 2)} + 1 \]

Order of Operations Steps

Let's break down how we can evaluate the expression step by step:

  1. Step 1: Evaluate the expression inside the exponent.

    • Expression: \( 3x - 2 \)

  2. Step 2: Multiply \( x \) by 3.

    • Expression: \( 3x \)

  3. Step 3: Subtract 2 from \( 3x \).

    • Expression: \( 3x - 2 \)

  4. Step 4: Evaluate \( 3^{(3x - 2)} \).

    • This is the operation that calculates the power.

  5. Step 5: Add 1 to the result of the exponentiation.

    • Expression: \( 3^{(3x - 2)} + 1 \)

Filling in the Table

| Step | Expression | Result | |--------|-----------------------------------|-------------| | Step 1 | \( 3x - 2 \) | | | Step 2 | \( 3x \) | | | Step 3 | \( 3x - 2 \) | | | Step 4 | \( 3^{(3x - 2)} \) | | | Step 5 | \( 3^{(3x - 2)} + 1 \) | |

Example Evaluation

To fill in the "Result" column, we can plug in a value for \( x \):

If we choose \( x = 1 \):

  1. Step 1 to Step 3:

    • \( 3(1) - 2 = 3 - 2 = 1 \)

  2. Step 4:

    • \( 3^{(3(1) - 2)} = 3^{1} = 3 \)

  3. Step 5:

    • \( 3 + 1 = 4 \)

If we want to fill in the "Result" column for \( x = 1 \):

| Step | Expression | Result | |--------|--------------------------------------|-------------| | Step 1 | \( 3x - 2 \) | 1 | | Step 2 | \( 3(1) \) | 3 | | Step 3 | \( 3 - 2 \) | 1 | | Step 4 | \( 3^{1} \) | 3 | | Step 5 | \( 3 + 1 \) | 4 |

You can apply other values for \( x \) in a similar manner! If you need any further assistance or clarifications, feel free to ask!