Graphing Rational Functions Flashcard Review

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

The general form of a rational function is $$f(x) = \frac{P(x)}{Q(x)}$$ , where $$P(x)$$ and $$Q(x)$$ are polynomials.

Vertical translation refers to shifting the graph of a function up or down on the coordinate plane.

The graph of $$f(x) = \frac{1}{x} + 3$$ is a vertical translation of the graph of $$f(x) = \frac{1}{x}$$ , moving it 3 units up.

The range of $$y = \frac{1}{x}$$ is all real numbers except 0, or $$y \ne 0$$ .

The domain of $$y = \frac{1}{x}$$ is all real numbers except 0, or $$x \ne 0$$ .

Inverse variation occurs when one variable increases while the other decreases, typically expressed as $$y = \frac{k}{x}$$ , where $$k$$ is a constant.

Yes, the equation $$y = \frac{10}{x}$$ shows inverse variation.

A vertical asymptote is a vertical line $$x = a$$ where a function approaches infinity or negative infinity.

A horizontal asymptote is a horizontal line $$y = b$$ that a function approaches as $$x$$ approaches infinity or negative infinity.