Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 2 to 4 and its y-axis ranges from negative 2 to 6, both by 1-unit increments. A curve is plotted in quadrant 1.
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The curve passes through left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 3 right parenthesis, and left parenthesis 4 comma 6 right parenthesis.

Given the graph of f(x)=3x−−√
, which of the following statements about the graph of g(x)=3x−−√3
must be true?

Option #1: Like f(x)
, g(x)
is also increasing.

Option #2: Like f(x)
, g(x)
has a domain of [0,∞]
.

Option #3: Like f(x)
, g(x)
has a range of [0,∞]
.

(1 point)
Option #
is the true statement about the graph.

Answer 1

Option #1.

Reason: f(x)=3√x and g(x)=∛(3x) are both increasing functions. g has domain and range all real numbers (odd root), so options 2 and 3 (domain [0,∞], range [0,∞]) are false.