Math Problem Statement

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

Solution

The question in the image asks:

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

Answer:

This statement is False.

In the equation f(x)=(xh)+kf(x) = (x - h) + k, the term hh represents a horizontal shift, not a vertical shift. The horizontal shift moves the graph left or right depending on the sign of hh. Specifically:

  • xhx - h indicates a shift to the right by hh units.
  • x+hx + h (i.e., if hh is negative) indicates a shift to the left by h|h| units.

The vertical shift is determined by the kk term, which shifts the graph up or down.


Would you like more details or have any further questions?

Related questions:

  1. What role does the kk in the equation f(x)=(xh)+kf(x) = (x - h) + k play?
  2. How does the transformation affect the graph of f(x)=xf(x) = x when hh 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 hh and kk are zero in f(x)=(xh)+kf(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.

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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