Key Features of Exponential Functions

Front

What is an exponential function?

Back

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 y-intercept of an exponential function?

Back

The point where the graph intersects the y-axis, typically found by evaluating f(0). For example, in f(x) = 3 * 2^x, the y-intercept is 3.

Front

What does the term 'domain' refer to in functions?

Back

The set of all possible input values (x-values) for the function.

Front

What does the term 'range' refer to in functions?

Back

The set of all possible output values (y-values) for the function.

Front

What is the x-intercept of an exponential function?

Back

Exponential functions do not have x-intercepts because they never touch the x-axis.

Front

What is the general shape of the graph of an exponential function?

Back

The graph rises rapidly to the right and approaches the x-axis but never touches it.

Front

What does it mean when x → -∞ in the context of exponential functions?

Back

It indicates that as x decreases without bound, the function approaches zero.

Front

What is the base of an exponential function?

Back

The constant b in the function f(x) = a * b^x, which determines the rate of growth or decay.

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

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).