EXPONENTIAL GRAPHS

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 shape of an exponential growth graph?

Back

The graph of an exponential growth function rises sharply as x increases, starting from a horizontal asymptote.

Front

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

Back

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

Front

What happens to f(x) as x approaches negative infinity in an exponential growth function?

Back

As x → -∞, f(x) approaches the horizontal asymptote, which is typically 0.

Front

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

Back

The horizontal asymptote of y = 2^x - 3 is y = -3.

Front

What is the behavior of an exponential decay function as x approaches infinity?

Back

As x → ∞, f(x) approaches the horizontal asymptote, which is typically a constant value.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

Front

What is the value of f(x) as x approaches infinity for the function y = 2^x?

Back

As x → ∞, f(x) approaches ∞.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches or crosses.

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase that occurs at a rate proportional to the current value, leading to rapid growth.