Domain and Range Exponential Functions

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the domain of the exponential function y=2^x?

Back

The domain is all real numbers, represented as (-∞, ∞).

Front

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

Back

The range is y > 0, meaning all positive real numbers.

Front

How does the graph of an exponential function behave as x approaches negative infinity?

Back

As x approaches negative infinity, the value of y approaches 0, but never reaches it (horizontal asymptote at y=0).

Front

What is an asymptote in the context of exponential functions?

Back

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

Front

What is the general form of an exponential function?

Back

The general form is y = a * b^x, where a is a constant, b is the base (b > 0), and x is the exponent.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.

Front

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

Back

The base determines the rate of growth or decay. If the base is greater than 1, the function grows; if the base is between 0 and 1, the function decays.

Front

What is the domain of the function f(x) = 3^x?

Back

The domain is all real numbers, represented as (-∞, ∞).