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

Front

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

Back

The y-intercept of an exponential function represents the initial value of the function when x = 0.

Front

What is the general form of an increasing exponential function?

Back

An increasing exponential function has a base greater than 1, typically written as f(x) = a(b^x) where b > 1.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote is a horizontal line that the graph of the function approaches but never touches, often represented as y = k where k is a constant.

Front

How do you find the y-intercept of the function y = 50(1.4)^x?

Back

To find the y-intercept, substitute x = 0: y = 50(1.4)^0 = 50.

Front

What is an exponential decay function?

Back

An exponential decay function is a function where the base is between 0 and 1, typically written as f(x) = a(b^x) where 0 < b < 1.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b^x) that indicates how much the function increases for each unit increase in x.

Front

Identify the y-intercept of the function f(x) = 13(0.27)^x.

Back

The y-intercept is 13, which is the initial value when x = 0.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

Front

What does the term 'asymptote' refer to in graphing?

Back

An asymptote is a line that a graph approaches but never touches, indicating a boundary for the function's values.