Graphing 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. The graph of a reciprocal function typically has vertical and horizontal asymptotes.

Front

What is the general form of a reciprocal function?

Back

The general form of a reciprocal function is f(x) = \frac{1}{x - h} + k, where (h, k) is the translation of the basic function f(x) = \frac{1}{x}.

Front

What does the vertical asymptote of a reciprocal function represent?

Back

The vertical asymptote occurs where the denominator of the function equals zero, indicating that the function approaches infinity.

Front

What does the horizontal asymptote of a reciprocal function represent?

Back

The horizontal asymptote represents the value that the function approaches as x approaches positive or negative infinity.

Front

How does shifting a reciprocal function to the right affect its graph?

Back

Shifting a reciprocal function to the right by h units results in the function f(x) = \frac{1}{x - h}, moving the vertical asymptote to x = h.

Front

How does shifting a reciprocal function up affect its graph?

Back

Shifting a reciprocal function up by k units results in the function f(x) = \frac{1}{x} + k, moving the horizontal asymptote to y = k.

Front

What is the effect of a negative sign in front of a reciprocal function?

Back

A negative sign in front of the reciprocal function, such as f(x) = -\frac{1}{x}, reflects the graph across the x-axis.

Front

What transformation occurs when the function is f(x) = \frac{1}{x + 2}?

Back

The function f(x) = \frac{1}{x + 2} shifts the graph left by 2 units.

Front

What transformation occurs when the function is f(x) = \frac{1}{x} + 3?

Back

The function f(x) = \frac{1}{x} + 3 shifts the graph up by 3 units.

Front

What is the domain of the function f(x) = \frac{1}{x - 2}?

Back

The domain of f(x) = \frac{1}{x - 2} is all real numbers except x = 2.