1. What Is Function Shift?

Function shift, also known as function transformation, involves moving a graph horizontally or vertically without changing its shape. The transformation follows the formula y = f(x - h) + k, where h represents horizontal shift and k represents vertical shift.

2. How The Calculator Works

The calculator uses the function shift formula:

Where:

• \( f(x) \) — Original function
• \( h \) — Horizontal shift (positive h shifts right, negative h shifts left)
• \( k \) — Vertical shift (positive k shifts up, negative k shifts down)
• \( x \) — Input value for evaluation

Explanation: The calculator evaluates the function at (x - h), then adds k to the result, giving you the transformed y-value.

3. Importance Of Function Transformation

Details: Understanding function shifts is fundamental in mathematics, particularly in graphing, calculus, and applied mathematics. It helps visualize how changes to a function's equation affect its graph.

4. Using The Calculator

Tips: Enter the function using standard mathematical notation (e.g., x^2, 2*x+1, sin(x)). Provide the horizontal and vertical shift values, and the x-value at which you want to evaluate the transformed function.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive h value do?
A: A positive h value shifts the graph to the right by h units.

Q2: What does a negative k value do?
A: A negative k value shifts the graph downward by |k| units.

Q3: Can I use trigonometric functions?
A: Yes, you can use functions like sin(x), cos(x), tan(x) if supported by the calculator's evaluation method.

Q4: What's the difference between f(x-h) and f(x)+k?
A: f(x-h) affects the horizontal position, while f(x)+k affects the vertical position of the graph.

Q5: How are function shifts used in real applications?
A: Function shifts are used in physics for wave transformations, in engineering for signal processing, and in economics for modeling shifted demand curves.