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 form of an exponential growth function?

Back

The general form is f(x) = a(b^x) where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form 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 range of an exponential function f(x) = a(b^x)?

Back

The range is y > 0 if a > 0, and y < 0 if a < 0.

Front

What is the y-intercept of the function f(x) = a(b^x)?

Back

The y-intercept is the value of f(0), which equals a.

Front

What is an asymptote in the context of exponential functions?

Back

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

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a(b^x) and the variable x is in the exponent.

Front

What is the effect of changing the base 'b' in an exponential function?

Back

Changing the base 'b' affects the rate of growth or decay; larger bases lead to faster growth.

Front

What is the domain of an exponential function?

Back

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