Write the function whose graph is the graph of y equals StartRoot x EndRoot but is shifted to the left 4 units.
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Part 1
yequals
  

​(Simplify your​ answer.)

To shift the graph of \( y = \sqrt{x} \) to the left by 4 units, we replace \( x \) with \( x + 4 \) in the function. This is because a horizontal shift to the left by \( h \) units is represented by \( x + h \).

Thus, the new function will be:

\[
y = \sqrt{x + 4}
\]

This is the equation of the function whose graph is the same as \( y = \sqrt{x} \) but shifted to the left by 4 units.

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you shift a graph to the right by a certain number of units?
2. What happens to the graph if you shift \( y = \sqrt{x} \) down by 3 units?
3. What is the domain of the function \( y = \sqrt{x+4} \)?
4. How does the graph of \( y = \sqrt{x} \) change if it's reflected over the x-axis?
5. How do you shift a function both horizontally and vertically at the same time?

**Tip:** Horizontal shifts are always counterintuitive: adding to \( x \) shifts the graph left, and subtracting from \( x \) shifts it right.

Write the function whose graph is the graph of y equals StartRoot x EndRoot but is shifted to the left 4 units.

Learn how to shift the square root function y = √(x) to the left by 4 units. This problem explains the transformation formula for horizontal shifts and walks you through the process of shifting graphs in algebra. Suitable for students in Grades 9-11.

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