If g(x) = f(bx) with 0 < b < 1, what happens to the graph of f?

• A. It is compressed horizontally by a factor of b.
• B. It is stretched horizontally by a factor of 1/b.
• C. It shifts to the right by b units.
• D. It reflects across the x-axis.

Answer: (B)

Multiplying the input by a number inside the function changes how the graph is scaled horizontally. For g(x) = f(bx) with 0 < b < 1, you’re effectively stretching the graph of f by a factor of 1/b. Here’s why: if a point (x0, y0) lies on f, then on g the corresponding point occurs where bx = x0, so x = x0/b and g(x) = f(bx) = f(x0) = y0. That means the same y-value occurs at a wider x-coordinate, pushed farther from the y-axis by the factor 1/b. Since 1/b > 1 when b is between 0 and 1, the graph spreads out horizontally rather than squeezing. So the graph of f becomes a wider version, stretched by a factor of 1/b.