Exponetial Functions Test Review

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 does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the value of a function decreases over time, typically represented by a base between 0 and 1 in the function f(x) = a * b^x.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is typically y = 0, indicating that as x approaches infinity, the function approaches but never reaches this value.

Front

How can you identify an exponential growth function?

Back

An exponential growth function can be identified by a base greater than 1 in the function f(x) = a * b^x, which results in the function increasing as x increases.

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 a > 0 and b > 1.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and are represented by a straight line, while exponential functions have a variable rate of change that increases or decreases exponentially.

Front

What is the significance of the base in an exponential function?

Back

The base of an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What type of function is represented by y = 7(5/4)^x?

Back

The function y = 7(5/4)^x is an exponential growth function because the base (5/4) is greater than 1.

Front

What does the term 'asymptote' refer to in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often y = 0.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where a is a constant and b is a positive real number.