Question

The dotted curve has arrows at both its ends and is labeled as g left parenthesis x right parenthesis equals negative root index 3 Start Root x End Root. The dotted curve starts in the second quadrant at approximately left parenthesis negative 2 comma 1.2 right parenthesis. The dotted curve decreases towards the origin, where it briefly, vertically extends downward in parallel with the y-axis before decreasing once more through the fourth quadrant past left parenthesis 1 comma negative 1 right parenthesis. The solid curve is labeled as f left parenthesis x right parenthesis equals negative Start Root x End Root. The solid curve starts at the origin and decreases through the fourth quadrant past left parenthesis 1 comma negative 1 right parenthesis. The solid curve has an arrow at its decreasing end.

Compare the graphs of f(x)=−x−−√
and g(x)=−x−−√3
. Which of the following features about the graphs is true?

(1 point)

The graphs have the same domains.

The graphs are both increasing.

The graphs have the same ranges.

The graphs are both decreasing.
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Answer 1

Correct statement: The graphs are both decreasing.

Reason: sqrt(x) and cube-root(x) are increasing, so negating them makes both -√x and -∛x decreasing. They do not have the same domain (f: x ≥ 0; g: all real x) and do not have the same range (f: (-∞, 0]; g: all real numbers).