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 growth 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 rate proportional to the current value, resulting in a rapid rise over time.

Front

Identify the characteristics of an exponential growth function.

Back

1. The function increases rapidly. 2. It has a horizontal asymptote. 3. The rate of growth accelerates as the value increases.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is a constant, 'b' is the base (b > 1 for growth), and 'x' is the exponent.

Front

How do you determine the base of an exponential function from a graph?

Back

The base can be determined by identifying the growth factor between points on the graph. If the function doubles every unit increase, the base is 2.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept represents the initial value of the function when x=0, which is equal to 'a' in the function f(x) = a * b^x.

Front

Explain the difference between linear and exponential growth.

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to much larger increases over time.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (f(x)) also increases.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is all positive real numbers (0, ∞).