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)
Responses

The graphs have different domains.
The graphs have different domains.

They are both decreasing on their domains.
They are both decreasing on their domains.

When x>1 , the function g(x)=2x−−√3 is greater than f(x)=2x−−√ .
When x greater than 1 , the function g left parenthesis x right parenthesis equals 2 root index 3 Start Root x End Root is greater than f left parenthesis x right parenthesis equals 2 Start Root x End Root .

Both graphs go through (−1,−1) , (0,0) , and (1,1) .
Both graphs go through left parenthesis negative 1 comma negative 1 right parenthesis , left parenthesis 0 comma 0 right parenthesis , and left parenthesis 1 comma 1 right parenthesis .

Answer 1

"The graphs have different domains." — f(x)=2√x has domain x ≥ 0, while g(x)=2∛x is defined for all real x.

(2) is false — both are increasing, not decreasing.
(3) is false — for x>1, √x > ∛x so f(x)>g(x).
(4) is false — e.g. f(1)=2 (not 1) and g(−1)=−2 (not −1).