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 an exponential function?

Back

'a' represents the y-intercept of the function, which is the value of the function when x = 0.

Front

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

Back

The y-intercept is 2.

Front

What is the base in the exponential function f(x) = 5 * 2^x?

Back

The base is 2.

Front

What does it mean if an exponential function is increasing?

Back

It means that as x increases, the value of f(x) also increases, indicating exponential growth.

Front

What does it mean if an exponential function is decreasing?

Back

It means that as x increases, the value of f(x) decreases, indicating exponential decay.

Front

How can you identify exponential growth from a graph?

Back

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

Front

How can you identify exponential decay from a graph?

Back

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

Front

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

Back

The graph of an exponential function is a smooth curve that either rises or falls, depending on whether it represents growth or decay.

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 exponentially.