Question

The solid curve is labeled f of x and passes through left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 2 right parenthesis, and left parenthesis 4 comma 4 right parenthesis. The dotted curve is labeled g of x and passes through left parenthesis 3.5 comma 3 right parenthesis, left parenthesis 2 comma 2.5 right parenthesis, left parenthesis 1 comma 2 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis negative 1 comma negative 2 right parenthesis, and left parenthesis negative 3.5 comma negative 3 right parenthesis.

Compare the given graphs of f(x)=2x−−√
and g(x)=2x−−√3
and determine which of the following is true.

(1 point)

They are both decreasing on their domains.

The graphs have different domains.

When x>1
, the function g(x)=2x−−√3
is greater than f(x)=2x−−√
.

Both graphs go through (−1,−1)
, (0,0)
, and (1,1)
.

Answer 1

Correct answer: The graphs have different domains.

Explanation: f(x) = 2√x has domain x ≥ 0, while g(x) = 2∛x has domain all real numbers. Both functions are increasing on their domains, so option 1 is false. For x > 1, 2√x > 2∛x (so option 3 is false). And neither function passes through (−1,−1) or (1,1) (option 4 is false).