Graphs of 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 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 rapidly as x increases, starting from a low value and approaching infinity.

Front

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

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching a horizontal asymptote.

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 where x = 0, which is (0, a).

Front

How do you find the y-intercept of the function y = 3^(x + 7) + 10?

Back

Substituting x = 0 gives y = 3^(0 + 7) + 10 = 3^7 + 10 = 2187 + 10 = 2197, so the y-intercept is (0, 2197).

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is the line that the graph approaches as x approaches infinity or negative infinity.

Front

What is the horizontal asymptote of the function f(x) = 3(2)^(x-4) + 5?

Back

The horizontal asymptote is y = 5.

Front

What type of function is f(x) = 2(1/7)^x?

Back

This is an exponential decay function because the base (1/7) is less than 1.

Front

What is the difference between exponential growth and exponential decay?

Back

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

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a * b^x, where b > 1.