GeoGebra Classroom

# Function Transformations

The applet below allows you to look at the effects on graphs of functions when stretched, compressed, or shifted vertically or horizontally. If f(x) is a function then: f(x + h) shifts f to the left by h units (or to the right if h is negative) f(bx + h) is equivalent to f(b(x + h/b)), which means that first the function is compressed by a factor of b (when b > 1) or stretched when 0 < b < 1. When b is negative, the function flips horizontally across a vertical line. a f(x) stretches f vertically when a is >1. When 0 < a < 1, the function is compressed vertically. When a is negative, the function flips across the y-axis f(x) + k shifts f k units up or down. ---------------- Using the applet:
• The function slider allows you to examine different parent functions.
• The phases slider allows you to break down the transformation a f(bx + h) + k to look at the effect of each on the equation and on the coordinates of an image point.
• The Point Calculation will take you back and forth between looking at the equation of the transformed function and looking at the calculation of the coordinates of the image point.
• The Reset button sets the values of a, b, h, and k back to their default settings.