Question

The dotted curve has arrows at both its ends and is labeled as g left parenthesis x right parenthesis equals 2 root index 3 Start Root x End Root plus 1. The dotted curve starts in the third quadrant at approximately left parenthesis negative 2 comma negative 2 right parenthesis. The dotted curve increases towards left parenthesis negative 1 comma 0 right parenthesis where it briefly, vertically increases in parallel with the y-axis. The dotted curve then increases through the second quadrant past left parenthesis 0 comma 2 right parenthesis. After passing through this point, the dotted curve increases into the first quadrant. The solid curve is labeled as f left parenthesis x right parenthesis equals 2 Start Root x plus 1 End Root. The solid curve starts at left parenthesis negative 1 comma 0 right parenthesis then increases through the second quadrant past left parenthesis 0 comma 2 right parenthesis. After passing through this point, the solid curve increases into the first quadrant, ending with an arrow at its increasing end.

Compare the graphs of f(x)=2x+1−−−−√
and g(x)=2x+1−−−−√3
. What is the y-intercept of both graphs?

(1 point)

Answer 1

Plug in x = 0.

f(0) = 2√(0+1) = 2·1 = 2
g(0) = 2∛(0+1) = 2·1 = 2

So both graphs have y-intercept (0, 2).