Graphing 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 is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, represented by a function of the form f(x) = a * b^x where b > 1.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, represented by a function of the form f(x) = a * b^x where 0 < b < 1.

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 the graph intersects the y-axis, which occurs at (0, a).

Front

How do you find the y-intercept of f(x) = 3^x?

Back

To find the y-intercept, substitute x = 0: f(0) = 3^0 = 1, so the y-intercept is (0, 1).

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is the horizontal asymptote of f(x) = 2(3^x)?

Back

The horizontal asymptote is y = 0, as the function approaches 0 as x approaches negative infinity.

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay rate; if the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

Front

What is the initial value in the function f(x) = 13(0.27)^x?

Back

The initial value is 13, which is the y-intercept of the function.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it is exponential growth; if the base is between 0 and 1, it is exponential decay.