Graphing 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 graph of a function approaches as x approaches infinity or negative infinity.

Front

How does the graph of y = 1/x shift if the function is y = 1/(x - 3)?

Back

The graph shifts right by 3 units.

Front

What happens to the graph of y = 1/x when multiplied by a negative number, such as y = -1/x?

Back

The graph reflects over the x-axis.

Front

What is the range of the function y = 1/x?

Back

The range is all real numbers except for 0.

Front

What transformation occurs in the function y = 1/(x + 2)?

Back

The graph shifts left by 2 units.

Front

What is the effect of adding a constant to a reciprocal function, such as y = 1/x + 2?

Back

The graph shifts up by 2 units.

Front

What is the domain of the function y = 1/x?

Back

The domain is all real numbers except for 0.