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 the output is the reciprocal of the input.

Front

What is the general shape of the graph of a reciprocal function?

Back

The graph of a reciprocal function has two branches, one in the first quadrant and one in the third quadrant, approaching the axes but never touching them.

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 a horizontal asymptote?

Back

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

Front

How does a vertical shift affect the graph of a reciprocal function?

Back

A vertical shift moves the graph up or down, changing the horizontal asymptote.

Front

What happens to the graph of a reciprocal function when it is compressed vertically?

Back

When compressed vertically, the branches of the graph become closer to the x-axis, making the function values smaller.

Front

What happens to the graph of a reciprocal function when it is stretched vertically?

Back

When stretched vertically, the branches of the graph move away from the x-axis, making the function values larger.

Front

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

Back

The domain is all real numbers except x = 0.

Front

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

Back

The range is all real numbers except y = 0.

Front

Describe the transformation: f(x) = 1/(x-2).

Back

This function is a horizontal shift of the basic reciprocal function f(x) = 1/x to the right by 2 units.