https://file.aiquickdraw.com/mathbot/file/17270525671663cgtpbjm.jpg

The question you uploaded asks: 

"If (0, 8) is a point on the graph of \( y = f(x) \), which of the following must be on the graph of \( y = f(-x) \)?"

### Solution:
1. **Understanding the relationship between \( f(x) \) and \( f(-x) \):**
   - The transformation \( y = f(-x) \) is a horizontal reflection of the graph of \( y = f(x) \) across the **y-axis**. 
   
2. **Given point:**
   - \( (0, 8) \) is on the graph of \( y = f(x) \), meaning \( f(0) = 8 \).

3. **Reflecting over the y-axis:**
   - When we reflect a point \( (a, b) \) across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.
   - In this case, the point \( (0, 8) \) is on \( f(x) \), and reflecting this point across the y-axis results in **no change** because the x-coordinate is 0. So, the point remains \( (0, 8) \).

Therefore, **(0, 8)** must also be on the graph of \( y = f(-x) \).

The correct answer is:
- **(0, 8)**.

Would you like more details or have any questions?

### 5 related questions:
1. What kind of transformation is \( f(-x) \) compared to \( f(x) \)?
2. How do vertical and horizontal transformations affect graphs of functions?
3. Can we apply this reflection concept to non-symmetric functions?
4. What happens to the graph of \( f(x) \) if the transformation is \( y = -f(x) \)?
5. How does the graph of \( y = f(x + 2) \) differ from \( y = f(x) \)?

### Tip:
When reflecting a graph horizontally (via \( f(-x) \)), only the x-coordinates change, while the y-coordinates stay the same.

If (0,8) is a point on the graph of y = f(x), which of the following must be on the graph of y = f(-x)?

Learn how to determine the points on the graph of y = f(-x) by reflecting the graph of y = f(x) across the y-axis. This problem explains how to find which point corresponds on f(-x) when given a point on f(x). Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation