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 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 steeply as x increases, starting from a low value and approaching infinity.

Front

What is the general shape of an exponential decay graph?

Back

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

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. For exponential functions, the horizontal asymptote is usually y = 0.

Front

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

Back

As x approaches infinity, f(x) approaches infinity.

Front

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

Back

As x approaches negative infinity, f(x) approaches the horizontal asymptote, which is typically y = 0.

Front

What is the base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth can be identified by a graph that rises sharply and continuously increases without bound.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay can be identified by a graph that falls sharply and approaches the x-axis but never touches it.

Front

What is the y-intercept of the function y = 2^(x-3)?

Back

The y-intercept occurs when x = 0. For y = 2^(0-3) = 2^(-3) = 1/8.