Which transformation affects the y-values of a function, producing vertical stretch or compression?

Which transformation affects the y-values of a function, producing vertical stretch or compression?

• A. Vertical Stretch/Compressions
• B. Horizontal Stretch/Compressions
• C. Rotation about the origin
• D. Translation up or down

Answer: (A)

Vertical stretch or compression changes the y-values by multiplying the outputs by a constant. If you start with y = f(x) and apply a factor a, you get y = a f(x). This scales every y-value: a > 1 stretches the graph vertically, 0 < a < 1 compresses it. The x-values stay the same because the input isn’t being altered. In contrast, changing x to cx or x/c would stretch or compress horizontally, rotation mixes x and y, and translating up or down adds a constant to y without scaling. So the operation that directly scales the y-values is the vertical stretch/compression.

Vertical stretch or compression changes the y-values by multiplying the outputs by a constant. If you start with y = f(x) and apply a factor a, you get y = a f(x). This scales every y-value: a > 1 stretches the graph vertically, 0 < a < 1 compresses it. The x-values stay the same because the input isn’t being altered. In contrast, changing x to cx or x/c would stretch or compress horizontally, rotation mixes x and y, and translating up or down adds a constant to y without scaling. So the operation that directly scales the y-values is the vertical stretch/compression.