Exponential Functions Day 1 Vocabulary

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 does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is a line that the graph approaches but never touches, typically y = 0 for functions of the form y = a(b^x).

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply to the right, indicating that as x increases, y increases rapidly.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply to the right, indicating that as x increases, y decreases rapidly.

Front

What is the range of an exponential function of the form y = a(b^x)?

Back

The range of an exponential function is (0, ∞) if a > 0, meaning y can take any positive value.

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 base in an exponential function?

Back

The base in an exponential function is the constant 'b' in the expression y = a(b^x), which determines the rate of growth or decay.

Front

What is the effect of changing the base in an exponential function?

Back

Changing the base affects the steepness of the graph; a larger base results in faster growth or decay.