Characteristics of Exponential Functions

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 a positive real number, and 'x' is the exponent.

Front

What is the general shape of an exponential growth function?

Back

The graph of an exponential growth function rises rapidly as x increases, starting from a low value and approaching infinity.

Front

What is the general shape of an exponential decay function?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching zero but never touching the x-axis.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

How do you find the horizontal asymptote of an exponential function?

Back

For exponential growth functions, the horizontal asymptote is typically y=0. For exponential decay functions, it is also y=0.

Front

What does it mean if a function has a horizontal asymptote at y=3?

Back

It means that as x approaches infinity or negative infinity, the value of the function approaches 3.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is (0, ∞), meaning it can take any positive value.

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is (0, L), where L is the horizontal asymptote.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the function increases rapidly, while exponential decay occurs when the function decreases rapidly.