If a vertical stretch by a factor of 2 is applied to a function, which best describes the effect on the graph?

If a vertical stretch by a factor of 2 is applied to a function, which best describes the effect on the graph?

• A. Compress vertically by factor 2
• B. Shift up by 2
• C. Stretch vertically by factor 2
• D. Reflect across x-axis

Answer: (C)

A vertical stretch multiplies every y-value by 2, so the graph gets taller while staying in the same horizontal position. In other words, each point (x, f(x)) moves to (x, 2f(x)), doubling its distance from the x-axis. This changes the height but not the width or position, and it does not flip the graph or shift it up or down. For example, a point at (3, 1) becomes (3, 2), and a point at (3, -4) becomes (3, -8). So the effect is a vertical stretch by factor 2.

A vertical stretch multiplies every y-value by 2, so the graph gets taller while staying in the same horizontal position. In other words, each point (x, f(x)) moves to (x, 2f(x)), doubling its distance from the x-axis. This changes the height but not the width or position, and it does not flip the graph or shift it up or down. For example, a point at (3, 1) becomes (3, 2), and a point at (3, -4) becomes (3, -8). So the effect is a vertical stretch by factor 2.