A9A Flashcard 1: Domain and Range of Exponential functions

Front

What is the range of an exponential function?

Back

The range of an exponential function is all real numbers greater than zero, expressed as y > 0.

Front

What inequality represents the range of f in an exponential function?

Back

The range can be represented as y ≥ k, where k is the minimum value of the function.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, expressed as x ∈ ℝ.

Front

What does the notation y > 0 indicate?

Back

It indicates that the output values of the function are always positive.

Front

How do you express the range of a function that starts at a minimum value?

Back

The range can be expressed as y ≥ minimum_value.

Front

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

Back

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

Front

What is an example of an exponential function?

Back

An example is f(x) = 2^x, where the base is 2.

Front

How do you find the range of the function f(x) = 3^x?

Back

The range is y > 0, as the function outputs positive values for all real x.

Front

What is the effect of changing the base of an exponential function?

Back

Changing the base affects the steepness of the curve; larger bases result in steeper growth.

Front

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

Back

An asymptote is a line that the graph approaches but never touches, typically the x-axis for exponential functions.