When y = a * f(x), multiply the y values of f(x) by a. Leave the x values alone. This is a vertical stretch (if |a| > 1) or shrink (if |a| < 1). Example: 1. Problem: Given is a graph of y = f(x). Sketch y = 2f(x). The figure below is the graph of f(x). Solution: Multiply values of
y by
2 and keep the same
x values. Then redraw the graph. The figure below is the graph of the solution.
When y = f(b * x), divide the x values of f(x) by b. Leave the y values alone. This is a horizontal stretch (if |b| < 1) or shrink (if |b| > 1). Example: 2. Problem: Given is a graph of y = f(x). Sketch y = f(.5x). The figure below is the graph of y = f(x). Solution: Divide each
x value by
.5 (same as multiplying by
2). Keep same
y values, and redraw the graph. The figure below is a graph of the solution.