Graphing Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the variable. The base 'b' determines the growth or decay of the function.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

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 f(x) = 13(0.5)^x?

Back

The horizontal asymptote is y = 0.

Front

How do you determine the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, expressed as (-∞, ∞).

Front

How do you determine the range of an exponential function?

Back

The range of an exponential function f(x) = a * b^x (where a > 0) is (0, ∞) for growth and (−∞, 0) for decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, causing the function to increase rapidly. Exponential decay occurs when the base 'b' is between 0 and 1, causing the function to decrease rapidly.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises steeply to the right and approaches the horizontal asymptote as it moves to the left.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function falls steeply to the right and approaches the horizontal asymptote as it moves to the left.