The following transformation were done to f(x)=x^3: right by 7 and flipped over x-axis

Given the function \( f(x) = x^3 \), we need to apply two transformations:

1. **Shift the function to the right by 7 units.**  
   To achieve this, we replace \( x \) with \( (x - 7) \). So the transformed function becomes:  
   \[
   f(x - 7) = (x - 7)^3
   \]

2. **Flip the function over the x-axis.**  
   To flip a function over the x-axis, we multiply the entire function by \(-1\). Thus, the final transformation becomes:  
   \[
   -f(x - 7) = -(x - 7)^3
   \]

So, the transformed function is:
\[
g(x) = -(x - 7)^3
\]

### Do you want more details or have any questions?

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Here are 5 related questions:

1. What happens when a function is shifted left instead of right?
2. How does a vertical flip affect the graph of different types of functions?
3. What is the effect of flipping a function over the y-axis?
4. How would the graph of \( f(x) = x^3 \) change if we reflected it over both the x-axis and y-axis?
5. How does horizontal scaling affect transformations?

**Tip:** For horizontal shifts, replacing \( x \) with \( (x - h) \) moves the graph right by \( h \) units. Replacing it with \( (x + h) \) moves the graph left.

The following transformations were done to f(x) = x^3: right by 7 and flipped over x-axis.

Learn how to transform the cubic function f(x) = x^3 by shifting it 7 units to the right and flipping it over the x-axis. This problem covers function transformations, including horizontal shifts and vertical flips, suitable for students in Grades 9-11.

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