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Level 528

Rational Functions


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horizontal asymptote
a line that the curve approaches as x goes to infinity but never reaches
vertical asymptote
comes from a factor in the denominator that doesnt cancel out
Excluded value
a value for which an expression is undefined
discontinuous
Features that fall into separate, non-overlapping groups
Hyperbola
Equation subtracts x²/a and y²/b=1; x and y coefficients have different signs.
branches
sections of a hyperbola that extend to infinity
rational function
a function which is the ratio of 2 polynomials
hole
excluded point
Branch
Each part of the graph of a reciprocal function.
Vertical Asymptotes
zeroes of denominator
zeros (x-intercepts)
Where numerator = zero
y-intercept
where x equals zero. Plug zero in for x, or just look at the constants of the function
real number
combonation of rational and irrational numbers
Rational Number
Any number that can be expressed as a ratio of two integers. Example; 6 can be expressed as 6/1, and 0.5 as 1/2.
Polynomial function
The graph crosses the x-axis up to n times and has up to n - 1 vertices (points where the function changes direction). The domain is all real numbers.
term of a polynomial
the parts of a polynomial separated by a + or -
degree
the highest power of a polynomial
leading coefficient
The coefficient of the term with the highest degree
X-intercepts
the point on a graph where y = 0, also points where the graph crosses the x-axis
Y-intercepts
sub 0 in for all x terms
Domain
The ______________________ is all the possible INPUT, X, values.
Range
The difference between the greatest number and the least number in a set of data.
vertical
The direction of something that runs north to south or south to north.
Horizontal
Straight line across from side to side (length)
slant
neither vertical nor horizontal
Asymptote
An imaginary line on a graph that acts as a boundary line.
end behavior asymptote
a value or function that the original function approaches but never attains as x approaches positive or negative infinity
slant asymptote
occurs when the degree of the top is higher than the degree of the bottom
intermediate behavior
the graphical behavior of a function that occurs between asymptotes
rational equation
an equation in one variable containing one or more rational expressions
rational inequality
any p(x)/h(x) < or > 0
extraneous solutions
when solving rational equations; check solutions for an undefined fraction.
constant term
the term without a variable
Continuity
Refers to whether a function contains holes, jumps, or breaks
Removable discontinuity
Occurs when common factors are cancelled in a rational expression.
How to recognize a hole
common factor on the numerator and denominator
How to find a hole
Set the factor = to 0 to solve for x coordinate. Simplify and plug x into the function to find y- coordinate
How to recognize a vertical asymptote
variable in the denominator that is not a common factor.
How to find a vertical asymptote
factor the denominator and set each factor = to 0
How to recognize a Horizontal Asymptote
Degree of numerator < or = degree of the denominator
y=0
Horizontal asymptote is degree of numerator = degree of the denominator
y= lc/lc
Horizontal Asymptote if degree of numerator<degree of denominator
How to recognize a Slant Asymptote
Degree of the numerator> degree of the denominator ( only if one degree greater)
How to find Slant Asymptote
Long Division. Divide number by the denominator to get equation of slant asymptote
x intercept
value of x where y = 0
y intercept
y value where the graph crosses the y axis