Question

Two parabolas with a common vertex are drawn on a coordinate plane. The x-axis ranges from negative 3 to 3 in one-unit increments and the y-axis ranges from negative 4 to 2 in one-unit increments.
▼Click for Long Desc
A solid parabola descends through left parenthesis negative 1.3 comma 2 right parenthesis, passes through left parenthesis negative 1 comma 0 right parenthesis, has a valley at vertex left parenthesis 0 comma negative 3 right parenthesis, rises through left parenthesis 1 comma 0 right parenthesis, and passes through left parenthesis 1.3 comma 2 right parenthesis. A dotted parabola descends through left parenthesis negative 2.6 comma 2 right parenthesis, left parenthesis negative 2 comma 0 right parenthesis, has a valley at vertex left parenthesis 0 comma negative 3 right parenthesis, rises through left parenthesis 2 comma 0 right parenthesis, and left parenthesis 2.6 comma 2 right parenthesis. All values are approximate.

Which of the following best describes the transformation from the solid-line graph to the dotted-line graph and correctly states the factor k?

(1 point)

horizontal compression with a factor k = 2

horizontal stretch with a factor k = 0.5

horizontal compression with a factor k = 0.5

horizontal stretch with a factor k = 2

Answer 1

Horizontal stretch by a factor of 2.

Reason: points move from x = ±1 to x = ±2 (and ±1.3 → ±2.6), so x-values are multiplied by 2. Equivalently y = f(x) becomes y = f(x/2).