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 steeply as x increases, showing a rapid increase in y values.

Front

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

Back

The graph of an exponential decay function falls steeply 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 f(x) = a * b^x is the point (0, a).

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

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, ∞).

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 y-intercept.

Front

How do you identify an exponential function from a graph?

Back

An exponential function can be identified by its characteristic curve that either rises steeply (growth) or falls steeply (decay) without ever touching the x-axis.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is the x-axis, or y = 0.