Which expression describes a vertical stretch of the graph by a factor a, where a > 1?

Which expression describes a vertical stretch of the graph by a factor a, where a > 1?

• A. g(x) = a f(x), a < 0
• B. g(x) = a f(x), a > 1
• C. g(x) = f(x) / a
• D. g(x) = f(x)

Answer: (B)

A vertical stretch means multiplying the y-values by a factor. When you apply a factor a to the outputs of f, you get g(x) = a f(x). If a > 1, each point (x, f(x)) moves to (x, a f(x)), pushing the graph away from the x-axis and making it taller. This is exactly the transformation described. The other forms don’t fit the idea of a pure vertical stretch by a factor greater than 1: using a negative would also flip the graph across the x-axis; dividing by a gives a smaller factor (a vertical compression when a > 1); and leaving it as f(x) means no change.

A vertical stretch means multiplying the y-values by a factor. When you apply a factor a to the outputs of f, you get g(x) = a f(x). If a > 1, each point (x, f(x)) moves to (x, a f(x)), pushing the graph away from the x-axis and making it taller. This is exactly the transformation described. The other forms don’t fit the idea of a pure vertical stretch by a factor greater than 1: using a negative would also flip the graph across the x-axis; dividing by a gives a smaller factor (a vertical compression when a > 1); and leaving it as f(x) means no change.