Exponential Functions: Graphs, Asymptotes and Transformations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What is the general shape of an exponential growth graph?

Back

An exponential growth graph rises steeply to the right and approaches the horizontal axis (y=0) as it moves to the left.

Front

What is the general shape of an exponential decay graph?

Back

An exponential decay graph falls steeply to the right and approaches the horizontal axis (y=0) as it moves to the left.

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

The horizontal asymptote is y = -4.

Front

How do you transform the function y = 2^x to shift it right by 3 units?

Back

The transformed function is y = 2^(x - 3).

Front

What does it mean for a graph to reflect across the line y=0?

Back

Reflecting across the line y=0 means that for every point (x, y) on the graph, there is a corresponding point (x, -y).

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the function increases as x increases, while exponential decay occurs when the function decreases as x increases.

Front

What is the effect of adding a constant to an exponential function?

Back

Adding a constant to an exponential function results in a vertical shift of the graph.

Front

What is the effect of subtracting a constant from an exponential function?

Back

Subtracting a constant from an exponential function results in a vertical shift downward of the graph.