Exponential Functions Review

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as D: All Real #'s.

Front

What is the range of an exponential function?

Back

The range of an exponential function is typically y > 0, meaning it only takes positive values.

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function increases rapidly and approaches the x-axis (y=0) but never touches it.

Front

What is an asymptote in the context of exponential functions?

Back

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

Front

How do you identify the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a(b^x) is found by evaluating f(0), which equals a.

Front

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

Back

Changing the base affects the growth rate: a larger base results in a steeper increase.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the base is greater than 1, while exponential decay occurs when the base is between 0 and 1.

Front

How do you find the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is typically y = 0.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b^x), where a is a constant and b is the base.

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase that occurs at a rate proportional to the value of the function, leading to rapid increases.