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 and .
Which of the following features about the graphs is true?
(1 point)
f (x) = − x−√ g (x) = − x−√
3
The graphs are both decreasing.
The graphs have the same domains.
The graphs have the same ranges.
The graphs are both increasing.

Answer 1

Answer: The graphs are both decreasing.

Reason: f(x) = −√x is decreasing on its domain x ≥ 0, while g(x) = −∛x is decreasing on all real x. Their domains differ (f: [0,∞), g: (−∞,∞)) and their ranges differ (f: (−∞,0], g: (−∞,∞)), so only the “both decreasing” statement is true.