Flashcard: Graphing/Characteristics of Exponentials

Front

What is the y-intercept of an exponential graph?

Back

The y-intercept of an exponential graph is at (0, 1).

Front

What does it mean if an exponential function has a negative sign in front of the variable x?

Back

It indicates that the exponential function is reflected across the y-axis.

Front

How can you determine if an exponential graph is increasing or decreasing?

Back

An exponential graph is increasing if the base of the exponent is greater than 1, and decreasing if the base is between 0 and 1.

Front

What is the horizontal asymptote of an exponential growth function?

Back

The horizontal asymptote of an exponential growth function is typically y = 0.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is typically y = 0.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = ab^x, where a is a constant and b is the base.

Front

What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay.

Front

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

Back

As x approaches infinity, the graph of an exponential growth function approaches infinity, while an exponential decay function approaches the horizontal asymptote.

Front

What is the effect of changing the value of 'a' in the exponential function y = ab^x?

Back

Changing the value of 'a' affects the vertical stretch or compression of the graph.

Front

What is the significance of the point (0, a) in the graph of an exponential function?

Back

The point (0, a) represents the y-intercept of the exponential function.