What’s the end behavior of g(x)=(5^x-3)+2.5

Hello from MrBillDoesMath!

  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