Exponetial Functions Test Review

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 decay function?

Back

The general form of an exponential decay function is f(x) = a * (1 - r)^x, where '0 < r < 1'.

Front

What is the y-intercept of an exponential function f(x) = a * b^x?

Back

The y-intercept is the value of f(0), which equals 'a'.

Front

How can you identify exponential growth?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1.

Front

How can you identify exponential decay?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a * b^x is between 0 and 1.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

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

Back

An asymptote is a line that a graph approaches but never touches, often the x-axis (y=0) for exponential decay.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, (-∞, ∞).

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is (0, a], where 'a' is the initial value.

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is (0, ∞).