Exercise 56 Page 280

Recall that the function g(x)=ab^(x-h) is a horizontal translation of the parent function f(x) = ab^x.

Example Function: g(x) = 4^(x-3)
Explanation: See solution.

Practice makes perfect

Let's start by reviewing the form of a horizontal translation of an exponential function.

The exponential function g(x)=ab^(x-h) is a horizontal translation of the parent function f(x) = ab^x. If h is positive the function is translated h to the right, and if it is negative it is translated \|h\| units to the left.

Therefore, to write a function that represents a horizontal translation of the parent function h(x) = 4^x, we just need to replace the argument x for x-h, where h is any nonzero real number. For example, g(x) = 4^(x-3). The graph of this new function is the same as h(x) but translated 3 units to the right.

Notice that there are infinitely many solutions satisfying the exercise's requirements. This is only an example.

Subchapter links

Communicate Your Answer p.273

Monitoring Progress p.274-277

Exercises p.278-280

Exercise 56 Page 280

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