An exponential function with a base of 3 has been vertically stretched by a factor of 1.5 and reflected in the y-axis. Its asymptote is the line y=2. Its y-intercept is (0,3.5). Write an equation of the function and state its domain and range.

Answer 1

y = 3^x
has asymptote y=0 and passes through (0,1)

y = 1.5 * e^3x passes through (0,3.5)

y = 3^x + 2 has asymptote y=2 and passes through (0,2)

y = 1.5 * 3^x + 2
has asymptote y=2
passes through (0,3.5)

y = 1.5 * 3^-x + 2
is the reflection. Same intercept, same asymptote.

see

http://www.wolframalpha.com/input/?i=plot+y+%3D+1.5+3^x+%2B+2%2C+y+%3D+1.5+3^-x+%2B+2

Answer 2

Alright thanks a lot :D