Assume that​ (a, b) is a point on the graph of f. What is the corresponding point on the graph of the following​ function?

yequals=f left parenthesis negative x right parenthesis

When dealing with the transformation \( y = f(-x) \), you are reflecting the graph of \( f(x) \) over the \( y \)-axis. This means that for every point \( (a, b) \) on the graph of \( f(x) \), the corresponding point on the graph of \( y = f(-x) \) will be \( (-a, b) \).

### Explanation:

- The function \( y = f(-x) \) takes the input \( x \) and negates it before applying the function \( f \).
- If \( (a, b) \) is on the graph of \( f(x) \), then \( b = f(a) \).
- For \( y = f(-x) \), you replace \( x \) with \( -x \) in the function, so \( y = f(-a) \).
- Thus, the point \( (a, b) \) on the graph of \( f(x) \) corresponds to the point \( (-a, b) \) on the graph of \( y = f(-x) \).

So, the corresponding point on the graph of \( y = f(-x) \) is \( \mathbf{(-a, b)} \).

Would you like further clarification on any aspect of this transformation or have any additional questions?

### Related Questions:
1. What is the effect on the graph of \( f(x) \) when applying the transformation \( y = -f(x) \)?
2. How does the transformation \( y = f(x - c) \) affect the graph of \( f(x) \)?
3. What happens to the graph of \( f(x) \) if the transformation \( y = f(-x) + k \) is applied?
4. If \( y = f(2x) \), how is the graph of \( f(x) \) affected?
5. What point corresponds to \( (a, b) \) on the graph of \( y = -f(-x) \)?

### Tip:
When dealing with transformations of functions, visualize how each change (reflection, shift, stretch, etc.) affects the graph. This approach can help you determine the corresponding points and understand the overall transformation better.

Explore how function transformation reflects points over the y-axis. Learn how to find corresponding points on graphs, using examples like y = f(-x). Suitable for high school students studying function transformations.

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