Exponential Functions

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, horizontal asymptotes often represent the value that the function approaches as x approaches infinity or negative infinity.

Front

What does the 'a' represent in the exponential function y = a(b^x)?

Back

'a' represents the y-intercept of the function, which is the value of y when x = 0.

Front

What is the general form of an increasing exponential function?

Back

An increasing exponential function can be expressed in the form y = a(b^x) where a > 0 and b > 1.

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 function?

Back

The range of an exponential function is all positive real numbers, expressed as (0, ∞).

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of 'a' in the function y = a(b^x).

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' in the function y = a(b^x) is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.

Front

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

Back

Changing the base 'b' affects the rate of growth or decay of the function. A larger base results in faster growth, while a base closer to 1 results in slower growth.

Front

What is the horizontal asymptote of the function y = a(b^x)?

Back

The horizontal asymptote is typically y = 0, as the function approaches this value as x approaches negative infinity.

Front

How can you identify an exponential function from a graph?

Back

An exponential function will show a rapid increase or decrease and will not have any linear segments. It will also have a characteristic curve that approaches a horizontal asymptote.