Transformations

As with all families of functions, exponentials can be transformed from their parent function to create new curves in other areas of the coordinate plane. Exponential functions can be translated up, down, left or right and reflected across the x or y-axis.

In order to graph the function y = 2^x + 4, the graph of y = 2^x is translated up 4 units on the coordinate plane. This will shift the asymptote of the graph from y = 0 to y = 4. Note on the table below, the y-intercept has shifted up 4 units from 1 to 5 and the decimal values are getting closer and closer to the number 4.

Therefore, adding a constant (k) will move the graph, and the horizontal asymptote up k units. Subtracting a constant (k) will move the graph, and the horizontal asymptote down k units.

As previously discussed, when the a-value is negative, the graph of the parent function will be reflected across the x-axis. The graphs below show the parent function, y = 2^xand the reflected curve y = -1(2^x).

When the exponent is negative, the graph will be reflected across the y-axis. The table and graph below represent the function, y = 5 ^-x. Notice in the table, when the x-values are negative, the opposite value of x will be positive, so the graph will grow quickly on the left-hand side. On the other hand, when the x-values are positive, the opposite value of x will be negative, so the graph will stay very close to the x-axis.

This type of function is known as exponential decay. Any function with a negative exponent or a b-value between 0 and 1 will create a curve that decreases from left to right.

To learn how to transform exponential functions, select the following links:

Transforming Exponentials #1

Transforming Exponentials #2

To solidify your understanding of transformations of exponential functions, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Exponential Functions Worksheet

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Exponential Functions Key

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