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 the base (a positive real number), and 'x' is the exponent.

Front

What does the 'a' represent in the exponential function f(x) = a * b^x?

Back

The 'a' represents the initial value or the y-intercept of the function.

Front

What is the common ratio in an exponential sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

Front

How do you identify exponential growth in a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Front

How do you identify exponential decay in a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where 0 < b < 1.

Front

If a function has a common ratio of 5, what type of function is it?

Back

It is an exponential growth function.

Front

What happens to the graph of an exponential function as x approaches negative infinity?

Back

As x approaches negative infinity, the value of the function approaches zero.

Front

What is the y-intercept of the function f(x) = 3 * 2^x?

Back

The y-intercept is 3, which occurs when x = 0.