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 is the general shape of an exponential growth graph?

Back

The graph of an exponential growth function rises rapidly as x increases, starting from a low value and approaching infinity.

Front

What is the general shape of an exponential decay graph?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching zero but never touching the x-axis.

Front

What does the y-intercept of an exponential function represent?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to the constant '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's output is zero, meaning the graph intersects the x-axis.

Front

How do 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's value increases rapidly.

Front

How do 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's value decreases rapidly.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, as x can take any value.

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is all positive real numbers, as the function approaches zero but never reaches it.

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is all positive real numbers, as the function approaches zero but never reaches it.