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Big Ideas Math Integrated I, 2016 View details

1. Exponential Functions

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Exercise 57 Page 280

Remember that vertical translations affect the entire function.

g(x) = 5^(x-3)+4

Practice makes perfect

We want to write a function for the indicated translation of the function f(x)=5^x. 4 units up and 3 units rightTo do so, we should recall two things.

If a vertical translation is up, we add to the y-variable. If the translation is down, we subtract from the y-variable.
If a horizontal translation is to the right, we subtract from the x-variable. If the translation is to the left, we add to the x-variable.

Therefore, for the indicated translation we have to add4 to the entire function, and subtract3 from the x-variable. f(x -3) +4 = 5^(x -3) +4 ⇔ g(x) = 5^(x -3) +4