Graphing Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = 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 y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the point where the graph intersects the y-axis, which occurs when x = 0. For y = a * b^x, the y-intercept is (0, a).

Front

What does exponential growth look like on a graph?

Back

Exponential growth is characterized by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Front

What does exponential decay look like on a graph?

Back

Exponential decay is characterized by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Front

What is the domain of the function y = 2^x?

Back

The domain of the function y = 2^x is all real numbers, expressed as (-∞, ∞).

Front

What is the range of the function y = 2^x?

Back

The range of the function y = 2^x is all positive real numbers, expressed as (0, ∞).

Front

What is an asymptote in the context of exponential functions?

Back

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

Front

How do you identify the initial value in an exponential function?

Back

The initial value in an exponential function f(x) = a * b^x is the value of 'a', which represents the y-intercept when x = 0.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function y = a * b^x. It determines how much the function increases for each unit increase in x.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.