Exponential Functions Key Features

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 the base (a positive real number), and 'x' is the exponent.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth (b > 1) or decay (0 < b < 1) factor.

Front

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

Back

The y-intercept represents the initial value of the function, which is the value of f(x) when x = 0.

Front

How do you find the y-intercept of the function f(x) = 10(5)^x?

Back

To find the y-intercept, substitute x = 0: f(0) = 10(5)^0 = 10.

Front

What is the asymptote of an exponential function?

Back

The asymptote of an exponential function is a horizontal line that the graph approaches but never touches, typically y = 0.

Front

What does it mean if an exponential function is increasing?

Back

An exponential function is increasing if the base 'b' is greater than 1, indicating that as x increases, f(x) also increases.

Front

What does it mean if an exponential function is decreasing?

Back

An exponential function is decreasing if the base 'b' is between 0 and 1, indicating that as x increases, f(x) decreases.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of an exponential function?

Back

The range of an exponential function is all positive real numbers, represented as (0, ∞).

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 when x = 0.