Exponential Graphs- asymptotes, domain, range

Front

What is an exponential growth graph?

Back

An exponential growth graph shows a rapid increase in value as the input (x) increases, typically represented by the function f(x) = a * b^x, where a > 0 and b > 1.

Front

What is an exponential decay graph?

Back

An exponential decay graph shows a rapid decrease in value as the input (x) increases, typically represented by the function f(x) = a * b^x, where a > 0 and 0 < b < 1.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.

Front

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

Back

The horizontal asymptote is y = -5.

Front

What is the vertical asymptote of the function f(x) = 1/(x + 4)?

Back

The vertical asymptote is x = -4.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is (0, ∞) if the function approaches a horizontal asymptote at y = 0.

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is (L, ∞) where L is the horizontal asymptote.

Front

How do you identify an exponential growth graph?

Back

An exponential growth graph rises steeply to the right and approaches a horizontal asymptote as x approaches negative infinity.

Front

How do you identify an exponential decay graph?

Back

An exponential decay graph falls steeply to the right and approaches a horizontal asymptote as x approaches positive infinity.