suppose (-11,3) is a point on the graph of y=f(x). What is a point that will be on the graph of y=f(-7x)+4?

To find the new point on the graph of \( y = f(-7x) + 4 \), given that \( (-11, 3) \) is a point on the graph of \( y = f(x) \), we need to understand how the transformations affect the point.

The transformation \( y = f(-7x) + 4 \) involves two operations:
1. **Horizontal stretch and reflection:** The \( -7x \) part indicates a reflection across the y-axis and a horizontal compression by a factor of 7.
2. **Vertical shift:** The \( +4 \) means a vertical shift of the graph 4 units upwards.

Now, apply these transformations to the given point \( (-11, 3) \):
1. Start with the x-coordinate. For the horizontal transformation, replace \( x \) in the expression with \( -7x \). Since \( x = -11 \),
   \[
   -7(-11) = 77
   \]
   So, the new x-coordinate is \( 77 \).
   
2. For the vertical transformation, the function is shifted 4 units upwards. Since \( f(-11) = 3 \), we add 4 to this value:
   \[
   3 + 4 = 7
   \]
   So, the new y-coordinate is \( 7 \).

Thus, the point \( (77, 7) \) will be on the graph of \( y = f(-7x) + 4 \).

Would you like further explanation or have any questions about this process?

Here are some related questions:
1. What happens when a graph is reflected across the y-axis?
2. How does horizontal compression affect the graph of a function?
3. What is the difference between a vertical shift and a horizontal shift in transformations?
4. How do we determine if a transformation results in a stretch or compression?
5. What are the steps to reverse a transformation on a graph?

**Tip:** When dealing with transformations, always apply horizontal changes first (reflections and stretches/compressions) before vertical shifts or reflections.

Suppose (-11,3) is a point on the graph of y=f(x). What is a point that will be on the graph of y=f(-7x)+4?

Discover how to find a new point on the transformed graph of y = f(-7x) + 4, starting from the given point (-11, 3) on y = f(x). This problem involves horizontal compression, reflection across the y-axis, and a vertical shift. Perfect for students in Grades 10-12.

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