VOCABULARY 1

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. In exponential functions, the horizontal asymptote is typically the x-axis (y=0).

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase that occurs at a constant percentage rate over a period of time, resulting in a rapid increase in value.

Front

Identify the characteristics of an exponential growth function.

Back

1. The function increases rapidly. 2. The rate of growth is proportional to its current value. 3. It has a horizontal asymptote.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where a is the initial value, b is the growth factor (b > 1), and x is the exponent.

Front

How can you determine the growth factor in an exponential function?

Back

The growth factor can be determined by the base of the exponent in the function's equation.

Front

What is the significance of the initial value in an exponential function?

Back

The initial value (a) represents the starting amount before any growth occurs.

Front

What does it mean if a function has a vertical asymptote?

Back

A vertical asymptote indicates a value of x where the function approaches infinity or negative infinity, often where the function is undefined.

Front

How do you graph an exponential growth function?

Back

1. Plot the initial value. 2. Use the growth factor to find additional points. 3. Draw a curve that approaches the horizontal asymptote.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster increases over time.

Front

What role does the base play in an exponential function?

Back

The base determines the rate of growth; a larger base results in faster growth.