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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