Question

The solid curve is labeled f of x and passes through left parenthesis 3 comma 2.7 right parenthesis, left parenthesis 2 comma 2.4 right parenthesis, and left parenthesis 0 comma 1 right parenthesis. The dotted curve is labeled g of x and passes through left parenthesis 3 comma 2.5 right parenthesis, left parenthesis 1 comma 2 right parenthesis, left parenthesis 0 comma 1 right parenthesis, left parenthesis negative 1 comma 0 right parenthesis, and left parenthesis negative 3 comma 0.3 right parenthesis.

Compare the graphs of f(x)=x−−√+1 and g(x)=x−−√3+1 . Which one of the following options is true?

(1 point)
Responses

Both functions are increasing on their domain.
Both functions are increasing on their domain.

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

Both functions have the same range, (−∞,∞) .
Both functions have the same range, left parenthesis negative infinity comma infinity right parenthesis .

Both functions have the same domain, x>0 .
Both functions have the same domain, x greater than 0 .

Answer 1

Answer: Both functions are increasing on their domain.

Reason: f(x)=√x+1 is increasing for x≥0 (√x grows as x increases). g(x)=∛x+1 is increasing for all real x (the cube root is strictly increasing). The other choices are false: they do not both pass through (−1,0) (f is not defined at −1), they do not have the same range (f has range [1,∞), g has range (−∞,∞)), and they do not have the same domain.