Rational Features

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Rational Features by Mind Map: Rational Features

1. intercepts

1.1. x-intercepts are a point or points on the line where the graph touches or crosses the x-axis

1.1.1. X-intercpets are found by plugging in 0 for "y" and then solving for "x"

1.2. y-interceps are a point or points on the line where the graph touches or crosses the y-axis

1.2.1. In order to find the y-intercepts of a graph one has to plug in 0 for the "x" values and solve for "y"

2. Asymptotes

2.1. An asymptote is an imaginary line that can never be crossed.

2.1.1. Vertical Asymptotes

2.1.1.1. Are straight lines of the equation , toward which a function f(x) approaches infinitesimally closely, but never reaches the line, as f(x) increases without bound

2.1.1.1.1. The vertical asymptotes of a rational function are found by using the zeros of the denominator.

2.1.2. Horizontal Asymptotes

2.1.2.1. A horizontal asymptote is a y-value on a graph which a function approaches but does not actually reach. Horizontal asymptotes are the only asymptotes that may be crossed.

2.1.2.1.1. •If the degree of the numerator is greater than the degree of the denominator by more than one, the graph has no horizontal asymptote.(none) • 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.(y = #) • If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is zero. (y = 0)

2.1.3. Oblique Asymptotes

2.1.3.1. An oblique asymptote occurs when the degree of the numerator is greater than the degree of the denominator by one, there is an oblique asymptote.

2.1.3.1.1. When finding the oblique asymptote, find the quotient of the numerator and denominator. If there are any remainders, disregard them. You only need the quotient.

3. Excluded values

3.1. Excluded values in polynomials are values that will make the denominator equal to zero

3.2. HOLES

3.2.1. Holes are the values that are shared by the numerator and the denominator that make the fraction equal to zero

3.2.1.1. To find holes in a function one has to factor and simplfy the equation and find the values that are similar between the numerator and the denominator