Graphing Rational Functions
Found 10 free book(s)Asymptotes, Holes, and Graphing Rational Functions
www.sctcc.eduAsymptotes, Holes, and Graphing Rational Functions Holes It is possible to have holes in the graph of a rational function. Before putting the rational function into lowest terms, factor the numerator and denominator. If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The
Asymptotes and Holes Graphing Rational Functions
online.math.uh.eduExercise Set 2.3: Rational Functions MATH 1330 Precalculus 229 Recall from Section 1.2 that an even function is symmetric with respect to the y-axis, and an odd function is symmetric with respect to the origin. This can sometimes save time in graphing rational functions. If a function is even or odd, then half of the function can be
4.4: Graphing Rational Functions Practice Date Period
www.birmingham.k12.mi.us4.4: Graphing Rational Functions Practice Identify the holes, vertical asymptotes, x-intercepts, horizontal asymptote, and domain of each. Then sketch the graph. 1) f (x) = 4 x − 3 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 2) f (x) = x2 + 7x + 12 −2x2 − 2x + 12 x y −8 −6 −4 −2 2 4 6 8 −8 −6 −4 −2 2 4 6 8 ...
MATH 1330 Precalculus - University of Houston
space.uh.eduExercise Set 2.3: Rational Functions..... 26 Exercise Set 2.4: Applications and Writing Functions ... function without graphing the points. 14. Determine whether or not each set of points represents a function without graphing the
Rational Expressions Worksheet
math.gmu.edu2. Simplify 2 2 2 9 4 3 x x x x 3. Simplify 2 3 1 3 x 4. Simplify 1 1 x y y x Graphing Rational Functions 1. Graph each equation. a. 1 y x y b. 1 x 2. Graph each equation.
Graphing Rational Functions.ks-ia2 - cdn.kutasoftware.com
cdn.kutasoftware.comGraphing Rational Functions Date_____ Period____ Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each. 1) f ( x) = x x Discontinuities: , Vertical Asym.: x , x Holes: None Horz. Asym.: y
GRAPHING RATIONAL FUNCTIONS
www.cbsd.orgGRAPHING RATIONAL FUNCTIONS To Identify Types of Discontinuity: Step 1: HOLES (Removable Discontinuities) Factor numerator & denominator Simplify If anything cancels, then there is a hole (More than one factor cancels More than one hole) Find the ordered pair, ( , ), substitute x into the SIMPLIFIED EQUATION to get y
Graphing Simple Rational Functions - cdn.kutasoftware.com
cdn.kutasoftware.comGraphing Simple Rational Functions Date_____ Period____ Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. 1) f (x) = − 4 x 2) f (x) = 4 x − 1 + 1 3) f (x) = − 3 x − 1 − 1 4) f (x) = − 3 x Identify the vertical asymptotes, horizontal asymptote, domain, and range of each. Then sketch the graph. 5) f (x ...
Rational Functions - Math
www.math.utah.eduRational Functions In this chapter, you’ll learn what a rational function is, and you’ll learn how to sketch the graph of a rational function. Rational functions A rational function is a fraction of polynomials. That is, if p(x)andq(x) are polynomials, then p(x) q(x) is a rational function. The numerator is p(x)andthedenominator is q(x ...
I. The Limit Laws
people.math.umass.eduMath131 Calculus I The Limit Laws Notes 2.3 I. The Limit Laws Assumptions: c is a constant and f x lim ( ) →x a and g x lim ( ) →x a exist Direct Substitution Property: If f is a polynomial or rational function and a is in the domain of f, then = f x lim ( ) x a