Graphing Rational Functions Ticket

Front

What is a horizontal asymptote?

Back

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

Front

How do you find the horizontal asymptote of a rational function?

Back

Front

What is a vertical asymptote?

Back

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.

Front

How do you find the vertical asymptote of a rational function?

Back

Front

What does it mean to translate a function?

Back

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

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Back

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

Front

What is the parent function of rational functions?

Back

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What are the steps to graph a rational function?

Back

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.

Front

What is the significance of intercepts in graphing rational functions?

Back

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

Front

What is the x-intercept of a function?

Back

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.