Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 3 to 3 and its y-axis ranges from negative 3 to 4, both by 1-unit increments. A dotted curve labeled g of x and a solid curve labeled f of x are plotted.
▶Click for Long Desc

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

(1 point)

Both functions are increasing on their domain.

Both functions go through the points (−1,0)
and (0,1)
.

Both functions have the same range, (−∞,∞)
.

Both functions have the same domain, x>0
.

Answer 1

Answer: Both functions are increasing on their domain.

Reason: f(x)=√x+1 is increasing for x≥0 (√x is increasing on [0,∞)), and g(x)=∛x+1 is increasing for all real x (∛x is increasing on (−∞,∞)). The other choices are false: only g passes through (−1,0); f(0)=g(0)=1 but f is undefined for x<0; f has range [1,∞) while g has range (−∞,∞); f’s domain is x≥0, not x>0.