Graphing Rational Functions Ticket

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

For a rational function of the form $$f(x) = \frac{p(x)}{q(x)}$$ , the horizontal asymptote can be determined by comparing the degrees of the polynomials p(x) and q(x). If the degree of p is less than the degree of q, the horizontal asymptote is y=0. If they are equal, the asymptote is y=\frac{a}{b}, where a and b are the leading coefficients.

A vertical asymptote is a vertical line that the graph of a function approaches as the input (x) approaches a certain value, typically where the function is undefined.

To find the vertical asymptote of a rational function $$f(x) = \frac{p(x)}{q(x)}$$ , set the denominator q(x) equal to zero and solve for x.

Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

The function is translated right 5 units and up 3 units.

The parent function of rational functions is $$y=\frac{1}{x}$$ .

1. Identify vertical and horizontal asymptotes. 2. Determine intercepts. 3. Analyze the behavior of the function around the asymptotes. 4. Plot additional points if necessary. 5. Draw the graph.

Intercepts (x-intercepts and y-intercepts) are points where the graph crosses the axes, providing key information about the function's behavior.

The x-intercept is the point where the graph of the function crosses the x-axis, found by setting f(x) = 0 and solving for x.