Exponential Functions: Translations
View the Lesson | MATHguide homepage Updated July 17th, 2022

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Use the graph of f(x) to the right to determine the translation:

g(x) = 5(2)x - 6 + 2.
Translation Statement for g(x):

“The exponential function f(x) = 2x must be shifted
units to the and
units and
vertically stretched by a factor of .”
Characteristics of g(x), to the nearest hundreth:

The domain is (-∞, +∞).
The range is (, +∞).
The asymptote is = .
The y-intercept is (, ).
The point (0,1) on f(x) shifts to (, ) on g(x).