Given three ordered pairs on *f* (*x*) = 3*x* + 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 is \( f(x) = 3x + 2 \), and we need to determine three image points on \( y = f(-x) \) for points A(1,5), B(3,11), and C(5,17).

1. For \( f(-x) \), we replace \( x \) with \( -x \) in the original function:
   \[
   f(-x) = 3(-x) + 2 = -3x + 2
   \]

2. Now, we'll apply the new function \( f(-x) = -3x + 2 \) to the x-values of points A, B, and C.

### Point A(1,5):
For \( x = 1 \),
\[
f(-1) = -3(1) + 2 = -3 + 2 = -1
\]
So, the image point is \( (1,-1) \).

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

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

Thus, the three image points are:

\[
(1,-1), (3,-7), (5,-13)
\]

Would you like further details or have any questions?

### Related Questions:
1. How does changing \( f(x) \) to \( f(-x) \) affect the graph of a linear function?
2. What are the key differences between \( f(x) \) and \( f(-x) \)?
3. How would you find the inverse of the function \( f(x) = 3x + 2 \)?
4. Can you determine the slope of the line \( y = f(-x) \)?
5. How would you determine if the points are collinear on the graph of \( y = f(-x) \)?

### Tip:
When reflecting a function across the y-axis, replacing \( x \) with \( -x \) flips the graph horizontally.

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).

Explore how to determine the image points for the reflection of a linear function f(x) = 3x + 2, across the y-axis. Calculate the image points of A(1,5), B(3,11), and C(5,17) on y = f(-x). This step-by-step solution involves applying the reflection concept and is ideal for students in Grades 8-10.

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