Given that f(x) = root x, the graph of function g can be produced as by transforming f as follows: Shifting f to the right 7 units, vertically stretching the result by a factor of 5. What is the formula for g?

To obtain the formula for the function \( g(x) \) by transforming the function \( f(x) = \sqrt{x} \), you need to apply the given transformations in the correct order.

1. **Shift to the right by 7 units**: To shift the function \( f(x) = \sqrt{x} \) to the right by 7 units, you replace \( x \) with \( x - 7 \). This gives you the intermediate function:
   \[
   h(x) = \sqrt{x - 7}
   \]

2. **Vertically stretch by a factor of 5**: To vertically stretch the function \( h(x) \) by a factor of 5, you multiply the entire function by 5. This gives you the final function:
   \[
   g(x) = 5\sqrt{x - 7}
   \]

Therefore, the formula for the function \( g(x) \) is:
\[
g(x) = 5\sqrt{x - 7}
\]

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. How would the graph change if the function were shifted to the left instead of to the right?
2. What happens to the graph if you compress it vertically instead of stretching it?
3. How would the function change if the vertical stretch factor was negative?
4. What is the domain of the function \( g(x) = 5\sqrt{x - 7} \)?
5. How would you find the range of \( g(x) \)?

**Tip:** When performing transformations, always apply horizontal shifts before vertical stretches or compressions for correct results.

Explore how to transform functions using shifts and stretches with this step-by-step solution. Learn how to shift a function to the right by 7 units and vertically stretch it by a factor of 5. Suitable for Grades 9-12.

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