Exponential Function Key Features

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point (0, a).

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions, the horizontal asymptote is typically y = 0.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a graph that rises steeply as x increases, showing a rapid increase in values.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a graph that falls steeply as x increases, showing a rapid decrease in values.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What is the equation of the horizontal asymptote for the function y = 2^x - 3?

Back

The horizontal asymptote is y = -3.