AP Precalculus Unit 2A 2.3 Essential Skills

These flashcards cover the essential knowledge and key characteristics of exponential functions as outlined in the lecture notes.

Exponential Function

A function in the form f(x) = ab^x, where a > 0 and b > 0.

Exponential Growth

When a > 0 and b > 1 in an exponential function.

Exponential Decay

When a > 0 and 0 < b < 1 in an exponential function.

Domain of Exponential Functions

The domain of an exponential function is all real numbers.

Output Values of Exponential Functions

These are proportional over equal-length input-value intervals.

Concavity of Exponential Functions

The graphs of exponential functions are always concave up (growth) or concave down (decay).

Extrema in Exponential Functions

Exponential functions do not have extrema except on a closed interval.

Points of Inflection in Exponential Functions

The graphs of exponential functions do not have points of inflection; they are always concave up or concave down.

Limit of Exponential Functions as x approaches infinity

As x increases, lim (x→∞) ab^x will increase or decrease without bound.

Limit of Exponential Functions as x approaches negative infinity

As x decreases, lim (x→−∞) ab^x approaches 0.

Additive Transformation of an exponential function

g(x) = f(x)+k is a vertical shift of the graph up or down, depending on the value of k. If the output values of g are proportional over equal-length input-values, then f is exponential.