Rational functions

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Rational functions by Mind Map: Rational functions

1. Intercepts (X and Y)

1.1. Y- Intercept

1.1.1. To find the y-intercept, substitute 0 for x and solve for y or f(x).

1.1.1.1. Definition: Are points were the graph crosses the y-axis

1.2. X- Intercept

1.2.1. To find the x-intercept (also known as zeros), substitute in 0 for y and solve for x.

1.2.1.1. Definition: Are points were the graph crosses the x- axis.

2. Vertical Asymptotes

2.1. How to get it: by the zeros or roots of the function or rational.

2.2. Vertical Asymptotes are straight lines that come close together with the original equation line but never reaches.

3. Slanted/Oblique Asymptotes

3.1. How to get it: when the degree of the numerator is greater than the degree of the denominator.

3.2. An Oblique Asymptote is la line y=mx+b. The line is neither horizontal or vertical

4. Holes

4.1. Definition: Holes are the zeroes in the numerator that repeat in the denominator.

4.2. How to get it: You get holes when the excluded values cancel out.

5. Horizontal asymptotes

5.1. If the degree of the numerator is greater than the degree of the denominator by more than, one, the graph has no horizontal asymptote.

5.2. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the two leading coefficients.

5.3. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is zero.

5.4. Definition: horizontal lines that the graph of the function approaches as x goes to +infinity or -infinity.