Math Problem Statement
Solution
The question in the image asks:
True or False? Given the base equation , the "h" determines a vertical shift.
Answer:
This statement is False.
In the equation , the term represents a horizontal shift, not a vertical shift. The horizontal shift moves the graph left or right depending on the sign of . Specifically:
- indicates a shift to the right by units.
- (i.e., if is negative) indicates a shift to the left by units.
The vertical shift is determined by the term, which shifts the graph up or down.
Would you like more details or have any further questions?
Related questions:
- What role does the in the equation play?
- How does the transformation affect the graph of when is positive or negative?
- Can you explain how vertical and horizontal shifts work together in transformations?
- What happens to the graph when both and are zero in ?
- 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.
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Transformations
Formulas
f(x) = (x - h) + k
Theorems
Transformation Theorem for Horizontal and Vertical Shifts
Suitable Grade Level
Grades 8-10