Question

Use the images to answer the question.

A curve passes through 7 plotted points on a coordinate plane with x and y axes ranging from negative 10 to 10 in unit increments.
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The equation is f left parenthesis x right parenthesis equals one fourth times x superscript 3. The coordinates of the plotted points are labeled as left parenthesis negative 3 comma negative 6 and three fourths right parenthesis, left parenthesis negative 2 comma negative 2 right parenthesis, left parenthesis negative 1 comma negative one fourths right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma one fourths right parenthesis, left parenthesis 2 comma 2 right parenthesis, and left parenthesis 3 comma 6 and three fourths right parenthesis.
A curve passes through 4 plotted points on a coordinate plane with x-axis ranging from negative 9 to 9 in increments of 1 and y-axis ranging from negative 11 to 11 in increments of 1.
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The equation is f left parenthesis x right parenthesis equals one half times start root x end root. The curve begins at the origin and has an arrow at the end. The coordinates of the plotted points are labeled as left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma one half right parenthesis, left parenthesis 4 comma 1 right parenthesis, and left parenthesis 9 comma 1 and one half right parenthesis.
Both graphs represent transformations from their respective parent functions. Describe the transformation.

(1 point)

Both graphs represent vertical compressions, with the same factors of k.

Both graphs represent vertical stretches, with the same factors of k.

Both graphs represent vertical compressions, although they use different factors of k.

Both graphs represent vertical stretches, although they use different factors of k.

Answer 1

Both graphs are vertical compressions (each y is multiplied by a factor k with 0<k<1), but the factors differ: 1/4 for x^3 and 1/2 for sqrt(x).