Which transformation affects the x-values, producing horizontal stretch or compression?

Which transformation affects the x-values, producing horizontal stretch or compression?

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

Answer: (B)

Changing the x-values means you’re altering the input to the function before you plot it. When you scale the input, distances along the horizontal axis change, producing a horizontal stretch or compression. This happens when you replace x with a·x or x/a in the function. - If you use a factor greater than 1 (like y = f(2x)), the graph gets squeezed toward the y-axis, so horizontal distances shrink. - If you use a factor between 0 and 1 (like y = f(x/2)), the graph stretches outward, so horizontal distances grow. This is the transformation that directly affects x-values. Other operations change other aspects: rotation moves points around the origin, vertical stretch/compression changes y-values, and translation left or right shifts the graph without changing its horizontal scale.

Changing the x-values means you’re altering the input to the function before you plot it. When you scale the input, distances along the horizontal axis change, producing a horizontal stretch or compression. This happens when you replace x with a·x or x/a in the function.

• If you use a factor greater than 1 (like y = f(2x)), the graph gets squeezed toward the y-axis, so horizontal distances shrink.

• If you use a factor between 0 and 1 (like y = f(x/2)), the graph stretches outward, so horizontal distances grow.

This is the transformation that directly affects x-values. Other operations change other aspects: rotation moves points around the origin, vertical stretch/compression changes y-values, and translation left or right shifts the graph without changing its horizontal scale.