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 steeply to the right and approaches the x-axis but never touches it.

Front

What is the general shape of an exponential decay graph?

Back

The graph of an exponential decay function falls steeply to the right and approaches the x-axis but never touches it.

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 'a' in the function f(x) = a * b^x.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions, the horizontal asymptote is usually the x-axis (y = 0).

Front

What is the horizontal asymptote of the function y = 2^x?

Back

The horizontal asymptote of the function y = 2^x is y = 0.

Front

What is the vertical asymptote of the function y = a * b^x?

Back

Exponential functions of the form y = a * b^x do not have vertical asymptotes.

Front

How do you determine if an exponential function is increasing or decreasing?

Back

An exponential function is increasing if the base 'b' is greater than 1 and decreasing if '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, ∞).