Reciprocal Functions

Front

What is a reciprocal function?

Back

A reciprocal function is a function of the form f(x) = 1/x, where x is not equal to zero.

Front

What is the vertical asymptote of a reciprocal function?

Back

The vertical asymptote of a reciprocal function occurs where the function is undefined, typically at x = 0.

Front

What is the horizontal asymptote of a reciprocal function?

Back

The horizontal asymptote of a reciprocal function is y = 0.

Front

How does the graph of f(x) = 1/x change when reflected over the x-axis?

Back

The graph becomes f(x) = -1/x, which flips the graph upside down.

Front

What happens to the graph of a reciprocal function when it is shifted up by 2 units?

Back

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

Front

What is the effect of shifting a reciprocal function left by 3 units?

Back

The new function becomes f(x) = 1/(x + 3), moving the graph left.

Front

What is the transformation of the function f(x) = 1/x reflected over the y-axis?

Back

The new function is f(x) = 1/(-x), which flips the graph horizontally.

Front

How do you find the vertical asymptote of the function f(x) = 1/(x - 7)?

Back

Set the denominator equal to zero: x - 7 = 0, so the vertical asymptote is x = 7.

Front

What is the transformation of the function f(x) = 1/x shifted down by 3 units?

Back

The new function is f(x) = 1/x - 3, moving the graph down.

Front

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

Back

The domain is all real numbers except x = 0.