Characteristics of Exponential Functions

Front

What is an exponential function?

Back

A mathematical function of the form y = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the range of an exponential function?

Back

The range of an exponential function is y > 0.

Front

What is the initial value in the function y = ⅓ × 4^x?

Back

The initial value is ⅓.

Front

What does exponential growth look like on a graph?

Back

Exponential growth is represented by a curve that rises steeply as x increases.

Front

What does exponential decay look like on a graph?

Back

Exponential decay is represented by a curve that falls steeply as x increases.

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 y = ⅓ × 4^x?

Back

The horizontal asymptote is y = 0.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Front

What is the base in an exponential function?

Back

The base is the constant b in the function y = a * b^x, which determines the rate of growth or decay.

Front

What is the effect of a base greater than 1 in an exponential function?

Back

A base greater than 1 indicates exponential growth.