Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It represents growth or decay processes.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = 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 y = a * b^x, where 0 < b < 1.

Front

What does the y-intercept of an exponential function represent?

Back

The y-intercept of an exponential function is the value of y when x = 0, which is equal to 'a' in the function y = a * b^x.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is (0, ∞).

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is (0, a), where 'a' is the initial value.

Front

What is the end behavior of an exponential growth function?

Back

As x → ∞, y → ∞; as x → -∞, y → 0.

Front

What is the end behavior of an exponential decay function?

Back

As x → ∞, y → 0; as x → -∞, y → ∞.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form y = a * b^x, where 'a' is a constant and 'b' is a positive real number.