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 exponent.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in f(x) = a * b^x is greater than 1, leading to an increase in value as 'x' increases. Exponential decay occurs when 'b' is between 0 and 1, resulting in a decrease in value as 'x' increases.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of the function y = 2^x?

Back

The range of the function y = 2^x is all positive real numbers, expressed as (0, ∞).

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 of the function f(x) = 13(0.5)^x is y = 0.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept of an exponential function, evaluate the function at x = 0. For example, in f(x) = a * b^x, the y-intercept is f(0) = a.

Front

What is the y-intercept of the function y = 3^x?

Back

The y-intercept of the function y = 3^x is (0, 1).

Front

What does the initial value of an exponential function represent?

Back

The initial value of an exponential function is the value of the function when x = 0, which is the y-intercept.

Front

What is the initial value of the function f(x) = 13(0.27)^x?

Back

The initial value of the function f(x) = 13(0.27)^x is 13.