Horizontal compression occurs when transforming g(x) = f(bx) with b > 1. Which term describes this change?

Horizontal compression occurs when transforming g(x) = f(bx) with b > 1. Which term describes this change?

• A. Horizontal stretch
• B. Vertical stretch
• C. Horizontal compression
• D. Vertical compression

Answer: (C)

When you scale the input inside a function, you change the graph horizontally. Multiplying x by a number greater than 1 inside the function means you reach the same output with smaller x-values, so features move closer to the y-axis. That is a horizontal compression, by a factor of 1/b. For example, if a feature occurs at x = 2 in f, it appears at x = 2/b in g; with b = 2, the feature is at x = 1. Vertical changes would involve scaling the output, not the input, and a horizontal stretch would come from using g(x) = f(x/b) with b > 1.

When you scale the input inside a function, you change the graph horizontally. Multiplying x by a number greater than 1 inside the function means you reach the same output with smaller x-values, so features move closer to the y-axis. That is a horizontal compression, by a factor of 1/b. For example, if a feature occurs at x = 2 in f, it appears at x = 2/b in g; with b = 2, the feature is at x = 1. Vertical changes would involve scaling the output, not the input, and a horizontal stretch would come from using g(x) = f(x/b) with b > 1.