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 general form of an exponential function?

Back

The general form is f(x) = a * b^x, where a is a non-zero constant and b > 0.

Front

What does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth (b > 1) or decay (0 < b < 1) factor 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 < ∞.

Front

What is the range of an exponential function?

Back

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

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches; for exponential functions, the horizontal asymptote is usually y = 0.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base b > 1, while exponential decay occurs when 0 < b < 1.

Front

How can you identify an exponential function from a graph?

Back

An exponential function graph will show a rapid increase or decrease, forming a curve that approaches a horizontal line (asymptote) but never touches it.

Front

What is the y-intercept of the function f(x) = 5^x?

Back

The y-intercept is the point where x = 0; for f(x) = 5^x, the y-intercept is (0, 1).

Front

What happens to the value of f(x) = 5^x as x approaches negative infinity?

Back

As x approaches negative infinity, f(x) approaches 0.