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Transformation Applicator for Exponential and Logarithmic Functions
Math Algebra • Exponential and Logarithmic Functions
Frequently Asked Questions
What does g(x) = A * f(k(x - h)) + v mean for exponential and logarithmic graphs?
It is a standard transformation model that scales, reflects, and shifts a base function f(x). A controls vertical scaling and reflection, k controls horizontal scaling and reflection, h shifts left/right, and v shifts up/down.
How are key points moved from the base graph to the transformed graph?
If (u, f(u)) is a point on the base curve, the transformed point is ((u / k) + h, A * f(u) + v) when k != 0. The calculator uses this mapping to place base and transformed key points on the same plot.
Why do the asymptotes change to y = v for exponentials and x = h for logarithms?
A basic exponential has a horizontal asymptote at y = 0, and adding v shifts the asymptote to y = v. A basic logarithm has a vertical asymptote at x = 0, and replacing x with (x - h) shifts it to x = h.
What is the domain condition for the transformed logarithmic function?
A logarithm requires a positive argument, so the input must satisfy k(x - h) > 0. That gives x > h when k > 0 and x < h when k < 0.
What base values are allowed when I choose a custom logarithm base b?
A valid logarithm base must satisfy b > 0 and b != 1. These restrictions ensure the logarithm is well-defined and not constant.