Exponential Graphs

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 does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises sharply as x increases, showing a J-shaped curve.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function falls sharply as x increases, approaching the x-axis but never touching it.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a * b^x.

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which the function f(x) = 0.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth can be identified by a curve that rises steeply to the right, indicating that the function increases rapidly.

Front

How can you identify exponential decay from a graph?

Back

Exponential decay can be identified by a curve that falls steeply to the right, indicating that the function decreases rapidly.

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.

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 growth function?

Back

The range of an exponential growth function is (0, ∞), meaning it only takes positive values.