Rational Functions Vocabulary

Rational Function

• the set of all output values / the set of all y-values

• the set of all input values / the set of all x-values

• a function that is written as a fraction where both the numerator and denominator are polynomials

• where the graph touches or crosses the x-axis

Domain

• the set of all output values / the set of all y-values

• the set of all input values / the set of all x-values

• a.      a function that is written as a fraction where both the numerator and denominator are polynomials

• where the graph touches or crosses the x-axis

Range

• the set of all output values / the set of all y-values

• the set of all input values / the set of all x-values

• a.      a function that is written as a fraction where both the numerator and denominator are polynomials

• where the graph touches or crosses the x-axis

Zeros/Roots

• the set of all output values / the set of all y-values

• the set of all input values / the set of all x-values

• a.      a function that is written as a fraction where both the numerator and denominator are polynomials

• where the graph touches or crosses the x-axis

Points of Discontinuity

• a dotted line that the ends of the graph approach

• where the graph is not continuous (there is a break in the graph)

• a dotted line that the graph approaches but never touches / occur at the x-value(s) that make the function undefined

• the x-values

Horizontal Asymptotes

• a dotted line that the ends of the graph approach

• where the graph is not continuous (there is a break in the graph

• a dotted line that the graph approaches but never touches / occur at the x-value(s) that make the function undefined

• the x-values

Vertical Asymptotes

• a dotted line that the ends of the graph approach

• where the graph is not continuous (there is a break in the graph

• a dotted line that the graph approaches but never touches / occur at the x-value(s) that make the function undefined

• the x-values

Which values are used when measuring the intervals of increase/decrease?

• y-intercepts

• x-intercepts

• the y-values

• the x-values

Extrema

• the point(s) where the graph changes directions forming a maximum or minimum

• negative and positive infinity

• the largest y-value

• the largest x-value

Which characteristic best describes the end behavior?

• Vertical asymptote

• Horizontal asymptote

• extrema

• y-intercept