Asked by Han
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.
Answers
Answered by
Steve
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
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
Answered by
Han
Alright thanks a lot :D
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