Horizontal Stretches and Compressions

For horizontal transformations of a function f(x): - g(x) = f(ax) where a > 1 compresses the graph horizontally by a factor of \frac{1}{a} - g(x) = f(\frac{x}{a}) where a > 1 stretches the graph horizontally by a factor of a.

Example: If f(x) = x^2, then g(x) = f(2x) = (2x)^2 = 4x^2 compresses the parabola horizontally by a factor of \frac{1}{2}

If f(x) = x^2, then g(x) = f(\frac{x}{3}) = (\frac{x}{3})^2 = \frac{x^2}{9} stretches the parabola horizontally by a factor of 3

Horizontal stretches and compressions affect how quickly the function changes as x increases, making the graph wider or narrower. When the coefficient inside the function is greater than 1, like f(2x), the graph compresses horizontally because the function reaches the same y-values in less horizontal distance.

Horizontal Stretches and Compressions is a Grade 11 math topic covered in enVision, Algebra 2 in Chapter 1: Linear Functions and Systems. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.

If f(x) = x^2, then g(x) = f(2x) = (2x)^2 = 4x^2 compresses the parabola horizontally by a factor of \frac{1}{2}; If f(x) = x^2, then g(x) = f(\frac{x}{3}) = (\frac{x}{3})^2 = \frac{x^2}{9} stretches the parabola horizontally by a factor of 3; For f(x) = |x|, the function g(x) = |4x| compresses the V-shape horizontally, making it narrower