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 form of a reciprocal function with a vertical shift?

Back

The general form is f(x) = 1/x + k, where k is the vertical shift.

Front

What happens to the graph of a reciprocal function when it is reflected over the x-axis?

Back

The graph of the function f(x) = 1/x becomes f(x) = -1/x, flipping it upside down.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a 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

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value.

Front

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

Back

The vertical asymptote is x = 2.

Front

How does a shift up by 2 units affect the reciprocal function f(x) = 1/x?

Back

The new function becomes f(x) = 1/x + 2, shifting the entire graph up by 2 units.

Front

What is the effect of a shift down by 2 units on the function f(x) = 1/x?

Back

The new function becomes f(x) = 1/x - 2, shifting the entire graph down by 2 units.

Front

What is the equation of the reciprocal function that has a vertical asymptote at x = 1 and a horizontal asymptote at y = 3?

Back

The equation is f(x) = 1/(x - 1) + 3.