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 and .
Which one of the following options is true?
(1 point)
f (x) = x + 1 −√ g (x) = x + 1 −√
3
Both functions have the same domain, x > 0.
Both functions go through the points (−1, 0) and (0, 1).
Both functions have the same range, (−∞, ∞).
Both functions are increasing on their domain.

Answer 1

None of the given options is true.

- They do not have domain x > 0 (both have the point (0,1), and g has points with negative x).
- Only g goes through (−1,0); f does not, so the “both go through (−1,0) and (0,1)” statement is false.
- Their ranges are not (−∞,∞); the plotted y-values lie in a small finite interval.
- g is not increasing on its whole domain (e.g. g(−3)=0.3 > g(−1)=0), so “both are increasing on their domain” is false.