Exponential Transformations

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers.

Front

What does a vertical translation up by 1 unit do to the graph of a function?

Back

It shifts the entire graph of the function up by 1 unit.

Front

What does a vertical translation down by 2 units do to the graph of a function?

Back

It shifts the entire graph of the function down by 2 units.

Front

What is a horizontal translation right by 1 unit?

Back

It shifts the entire graph of the function to the right by 1 unit.

Front

What is a horizontal translation left by 2 units?

Back

It shifts the entire graph of the function to the left by 2 units.

Front

What is the parent function of an exponential function?

Back

The parent function of an exponential function is y = a^x, where a > 0.

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.

Front

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

Back

The horizontal asymptote is y = -3.

Front

How does the graph of y = 3^x - 1 differ from y = 3^x?

Back

The graph of y = 3^x - 1 is shifted down by 1 unit compared to y = 3^x.

Front

What happens to the graph of y = 3^x when x is increased?

Back

The graph increases rapidly as x increases.