Given three ordered pairs on f (x) = 3x + 2, determine three image points on y = f (-x). A(1,5), B(3,11),C(5,17). Make sure they are in parentheses with no spaces, that is in the form (a,b).

We are given that the function \( f(x) = 3x + 2 \), and the points A(1, 5), B(3, 11), and C(5, 17) lie on the graph of \( f(x) \).

Now, we want to find the corresponding image points on \( y = f(-x) \). To do this, we substitute \( -x \) for \( x \) in the function, so \( f(-x) = 3(-x) + 2 = -3x + 2 \).

### Step-by-step solution:

1. **For Point A (1, 5):**
   \[
   y = f(-1) = -3(1) + 2 = -3 + 2 = -1
   \]
   So, the new point is \( (1, -1) \).

2. **For Point B (3, 11):**
   \[
   y = f(-3) = -3(3) + 2 = -9 + 2 = -7
   \]
   So, the new point is \( (3, -7) \).

3. **For Point C (5, 17):**
   \[
   y = f(-5) = -3(5) + 2 = -15 + 2 = -13
   \]
   So, the new point is \( (5, -13) \).

### Final Image Points:
- \( (1,-1) \)
- \( (3,-7) \)
- \( (5,-13) \)

Would you like further explanation or details on any step?

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Here are 5 related questions for deeper understanding:
1. How would you derive the inverse of \( f(x) = 3x + 2 \)?
2. What happens if we reflect the function across the line \( y = x \)?
3. What is the effect of transforming the function into \( f(ax) + b \)?
4. Can you find the image points for \( f(x) = -3x + 2 \)?
5. How would the graph of \( f(x) = 3x + 2 \) look when reflected over the y-axis?

**Tip:** Replacing \( x \) with \( -x \) reflects the graph of the function across the y-axis.

Given three ordered pairs on f(x) = 3x + 2, determine three image points on y = f(-x). A(1,5), B(3,11), C(5,17). Make sure they are in parentheses with no spaces, that is in the form (a,b).

Learn how to determine image points on y = f(-x) for given ordered pairs on f(x) = 3x + 2. This problem covers concepts of function transformations, including reflections over the y-axis, suitable for students in Grades 9-10.

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