Graphing Simple Exponential Functions

Front

What is exponential decay?

Back

Exponential decay is a decrease in a quantity by a consistent percentage over a period of time, represented by the function y = a * b^x where 0 < b < 1.

Front

What is exponential growth?

Back

Exponential growth is an increase in a quantity by a consistent percentage over a period of time, represented by the function y = a * b^x where b > 1.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. In exponential functions, it often represents a horizontal line that the function approaches as x approaches infinity.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is y = b^x, where b is a positive constant.

Front

How does a vertical shift affect the graph of an exponential function?

Back

A vertical shift moves the graph up or down. For example, y = b^x + k shifts the graph k units up if k > 0 and k units down if k < 0.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = b^x is always (0, 1) because b^0 = 1.

Front

What happens to the graph of y = 3^x as x approaches negative infinity?

Back

As x approaches negative infinity, the graph of y = 3^x approaches the asymptote at y = 0.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function y = a * b^x, which determines how quickly the function increases.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases exponentially.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a graph that decreases rapidly at first and then levels off, approaching the horizontal asymptote.