EXPONENTIAL GRAPHS

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 the base (a positive real number), and x is the exponent.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises rapidly as x increases, approaching infinity, and has a horizontal asymptote.

Front

What is the horizontal asymptote of the function y = 2^x?

Back

The horizontal asymptote of the function y = 2^x is y = 0.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

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 or crosses.

Front

What happens to the value of an exponential function as x approaches negative infinity?

Back

As x approaches negative infinity, the value of an exponential function with a base greater than 1 approaches 0.

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

How can you identify an exponential function from its equation?

Back

An exponential function can be identified by the variable x being in the exponent, such as in y = 2^x.

Front

What is the y-intercept of the function y = 2^x?

Back

The y-intercept of the function y = 2^x is (0, 1), since 2^0 = 1.

Front

What is the domain of an exponential function?

Back

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