AP Precalculus Unit 2A: 2.4 Exponential Function Manipulation

These flashcards cover key properties and concepts related to exponential functions as discussed in the lecture notes.

Product Property for Exponents

States that b^mbⁿ = b^m+n  

Power Property for Exponents

States that (b^m)ⁿ = b^mn .

Negative Exponent Property

States that b^-n = (1/b)ⁿ

Horizontal Translation

Every translation of an exponential function of the form f(x) = b^(x+k) is equivalent to a vertical dilation:

f(x) = b^(x+k) = b^xb^k = ab^x, where a = b^k.

kth Root of b

b^(1/k) is the kth root of b, where k is a natural number and the root exists

Horizontal Dilation

Every horizontal dilation of an exponential function, f(x) = b^(cx) is equivalent to a change of the base of an exponential function:

f(x) = (b^c)^x, where b^c is a constant and c ≠ 0.