Horizontal Asymptotes of Exponential Functions

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.

Front

How do you find the horizontal asymptote of an exponential function of the form y = a * b^x?

Back

For exponential functions of the form y = a * b^x, the horizontal asymptote is y = 0 if b > 1 and y = a if b < 1.

Front

What is the horizontal asymptote of the function y = 2 * (1/3)^x?

Back

The horizontal asymptote is y = 0.

Front

What is the horizontal asymptote of the function y = 5 * 2^x?

Back

The horizontal asymptote is y = 0.

Front

True or False: The horizontal asymptote of an exponential function can be a vertical line.

Back

FALSE

Front

What does it mean if a function has a horizontal asymptote at y = k?

Back

It means that as x approaches positive or negative infinity, the function's value approaches k.

Front

For the function y = 3 * e^(-x), what is the horizontal asymptote?

Back

The horizontal asymptote is y = 0.

Front

What is the horizontal asymptote of the function y = -4 * 2^x?

Back

The horizontal asymptote is y = 0.

Front

True or False: The horizontal asymptote can be above the x-axis.

Back

TRUE

Front

What is the horizontal asymptote of the function y = 6?

Back

The horizontal asymptote is y = 6.