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Graphing the Transformed Exponential Function. • The domain is always {x ε R}. Transformations do not change the domain. • The range depends on the location of ...
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All exponential functions can be written in the form:
where “b” is the base of the exponential equation, y = bx.
Example One Determine the base function of following exponential functions and then determine the transformations of each base function.
Base Function: Base Function:
Transformations: Transformations:
Note : on a graph of an exponential function, the asymptote will occur along the line y = c.
Example Two Determine the equations of the exponential function that have the following properties: a) Function One a. A base of 3 b. Vertically stretched by a factor of 2 c. Vertically translated 3 units up d. A reflection in the x-axis
b) Function Two a. A base of 2 b. Stretched vertically by a factor of 1. c. Reflected in the y-axis d. Its asymptote is the line y = 2
Graphing the Transformed Exponential Function The domain is always {x ε R}. Transformations do not change the domain. The range depends on the location of the horizontal asymptote and whether the function is above or below the asymptote. If it is above the asymptote, its range is y > c. If it is below, its range is y < c. Apply each transformation one at a time, in the order: a, k, d, c. You may need to factor the exponent to see what the exact transformations are. For