Graphs of Reciprocal Functions

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/x, where x is not equal to zero.

Front

What is the domain of the reciprocal function f(x) = 1/x?

Back

The domain is all real numbers except x = 0.

Front

What is the range of the reciprocal function f(x) = 1/x?

Back

The range is all real numbers except y = 0.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

What is the vertical asymptote of the function f(x) = 1/(x-2)?

Back

The vertical asymptote is x = 2.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the function approaches as x approaches infinity or negative infinity.

Front

What is the horizontal asymptote of the function f(x) = 1/x?

Back

The horizontal asymptote is y = 0.

Front

How does the graph of f(x) = 1/x behave as x approaches 0 from the left?

Back

As x approaches 0 from the left, f(x) approaches negative infinity.

Front

How does the graph of f(x) = 1/x behave as x approaches 0 from the right?

Back

As x approaches 0 from the right, f(x) approaches positive infinity.

Front

What happens to the graph of f(x) = 1/x as x approaches positive infinity?

Back

As x approaches positive infinity, f(x) approaches 0.