Question

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

(1 point)
Responses

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 .

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

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

Answer 1

"The graphs have different domains." — correct.

Reason: f(x) = 2√x has domain x ≥ 0, while g(x) = 2∛x is defined for all real x, so the domains differ. Both functions are increasing on their domains (not decreasing). For x > 1, f(x) > g(x) (for example x = 8: f(8) = 2√8 ≈ 5.66, g(8) = 2∛8 = 4). Also they do not pass through (−1,−1) or (1,1) — e.g. f(1) = g(1) = 2, and g(−1) = −2.