Question

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 = 0.5

horizontal compression with a factor k = 2

horizontal stretch with a factor k = 2

horizontal stretch with a factor k = 0.5

Answer 1

Horizontal stretch by a factor k = 2.

Explanation: every x-value doubles (1 → 2, 1.3 → 2.6, −1 → −2, etc.), so the dotted graph is y = f(x/2), a horizontal stretch of the solid graph by 2.