Question

for f(x)=(x+1)^3, with domain {x:x > 1} how is the range {y:y > 8}? The answer was the range, but I can't figure out how the computer got that.. I graphed y=(x+1)^3 on my graphing calculator and assumed that the answer was {y:y > 1} because that was where the graph intersected the y-axis. Can someone help me understand what I did wrong and what I need to do to get it right?

Answer 1

If x = 1, then

f(x) = (x+1)^3

f(1) = (1+1)^3

f(1) = 2^3

f(1) = 8

So the point (1, 8) is on the graph. Since x = 1 is the boundary of the domain, the boundary of the range is y = 8

And because this function is increasing when x > 1, the range is the set {y: y > 8}, basically any y value greater than 8.

Answer 2

Thank you so much! :D

Answer 3

np