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The problem on the page involves applying transformations to given linear functions and graphing them. Let's go over each subpart of the question:

### Part A
- **Original Function:** \( f(x) = 3x + 3 \)
- **Transformation:** Graph \( f(x) - 3 \).

To apply this transformation, we subtract 3 from the \( y \)-values of the original function. This is a vertical shift downward by 3 units. 

### Part B
- **Original Function:** \( f(x) = x + 7 \)
- **Transformation:** Graph \( -2f(x) \).

This transformation involves two steps:
1. Multiply the original function by -2, which reflects the graph across the x-axis and vertically stretches it by a factor of 2.
   \[
   f(x) = x + 7 \quad \Rightarrow \quad -2f(x) = -2(x + 7) = -2x - 14
   \]
   
### Part C
- **Original Function:** \( f(x) = 2x + 1 \)
- **Transformation:** Graph \( 2f(x) + 3 \).

This transformation scales the graph vertically by a factor of 2 and then shifts it upwards by 3 units. The equation becomes:
   \[
   f(x) = 2x + 1 \quad \Rightarrow \quad 2f(x) + 3 = 2(2x + 1) + 3 = 4x + 2 + 3 = 4x + 5
   \]

For each case, the transformed graphs need to be sketched accordingly.

Would you like further clarification on any of the transformations or specific details for graphing them? Here are 5 questions you can think about:

1. What is the effect of multiplying a function by a negative number on its graph?
2. How do vertical shifts and stretches affect the slope of a line?
3. What does reflecting a graph across the x-axis do to its points?
4. Can you explain the difference between a vertical and a horizontal transformation?
5. How does adding a constant to a function's output affect the function's graph?

**Tip:** When dealing with function transformations, always consider how each operation (e.g., addition, multiplication) modifies the graph, either by shifting, stretching, or reflecting.

For each of the following, a function has been given along with its graph. Perform the specified transformation of the function and graph.

Explore linear function transformations, including vertical shifts, reflections over the x-axis, and vertical stretches. This lesson focuses on applying transformations to functions such as f(x) = 3x + 3 and graphing the results. Suitable for students in Grades 9-11.

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