Hello from MrBillDoesMath!
Answer: g(x) approaches "infinity' as x approaches "positive infinity" and g(x) approaches --0.5 as x approaches "negative infinity"
Discussion.
g(x) = ( 5^x -3) + 2.5
Suppose x is approaching positive infinity. Then the term 5^x grows without bound ("positive infinity") so the -3 and "2.5" constants have no impact at all. That is, g(x) behaves like 5^x which grows without bound.
Suppose x is approaching negative infinity. Then 5^x approaches 0 (zero) so g(x) approaches
(0 -3) + 2.5 -
= - 0.5
Thank you,
MrB
