Transformations of Reciprocal Functions

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/g(x), where g(x) is a non-zero function.

Front

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

Back

The graph of a reciprocal function typically has two branches, approaching the x-axis and y-axis asymptotically.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

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

Back

The horizontal asymptote is y = 0.

Front

What does it mean to shift a graph up by 2 units?

Back

Shifting a graph up by 2 units means adding 2 to the y-values of the function.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

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

Back

The domain is all real numbers except x = 2.

Front

What is the effect of a vertical shift on a reciprocal function?

Back

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

Front

What happens to the graph of f(x) = 1/x when it is reflected over the y-axis?

Back

The graph remains unchanged because f(x) = 1/x is an even function.

Front

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

Back

The vertical asymptote is x = 2.