The Reciprocal Function Family

Front

What is the reciprocal function?

Back

The reciprocal function is defined as 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

Describe the transformation: f(x) = 1/(x - 3).

Back

This function is a horizontal shift to the right by 3 units.

Front

Describe the transformation: f(x) = -1/x.

Back

This function is a reflection over the x-axis.

Front

What happens to the graph of f(x) = 1/x when x approaches 0?

Back

The graph approaches infinity or negative infinity, indicating a vertical asymptote.