https://file.aiquickdraw.com/mathbot/file/1727708895684a0zpa2zg.jpg

The question in the image asks:

**True or False?**
Given the base equation \( f(x) = (x - h) + k \), the "h" determines a vertical shift.

### Answer:
This statement is **False**.

In the equation \( f(x) = (x - h) + k \), the term **\( h \)** represents a **horizontal shift**, not a vertical shift. The **horizontal shift** moves the graph left or right depending on the sign of \( h \). Specifically:
- \( x - h \) indicates a shift to the **right** by \( h \) units.
- \( x + h \) (i.e., if \( h \) is negative) indicates a shift to the **left** by \( |h| \) units.

The **vertical shift** is determined by the \( k \) term, which shifts the graph **up or down**.

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Would you like more details or have any further questions?

### Related questions:
1. What role does the \( k \) in the equation \( f(x) = (x - h) + k \) play?
2. How does the transformation affect the graph of \( f(x) = x \) when \( h \) is positive or negative?
3. Can you explain how vertical and horizontal shifts work together in transformations?
4. What happens to the graph when both \( h \) and \( k \) are zero in \( f(x) = (x - h) + k \)?
5. How do other transformations like reflections and stretches affect the graph of a function?

### Tip:
Always check whether transformations like shifts affect the function inside or outside the parentheses; it determines whether they are horizontal or vertical shifts.

True or False? Given the base equation f(x) = (x - h) + k, the "h" determines a vertical shift.

This problem explores the horizontal and vertical shifts in the function f(x) = (x - h) + k. Learn why 'h' represents a horizontal shift while 'k' determines the vertical shift. Suitable for students in Grades 8-10.

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