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vert asymptotes and holes
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Horizontal and Vertical Asymptotes Vertical Asymptote A term which results in zero in the denominator causes a vertical asymptote when the function is graphed ...
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oblique asymptote vertical asymptote Oblique Asymptotes To find the equation of an oblique asymptote, ...
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Rational Expressions, Vertical Asymptotes, and Holes Find all asymptotes & holes & then graph: * Rational Expression It is the quotient of two polynomials.
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Section 2.6 Rational Functions and Asymptotes A rational function is a function written in the form of a polynomial divided by a polynomial. Domain: is the x-values ...
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Chapter 3 Limits and Horizontal Asymptotes: Limits at Infinity Revisited Limits at Infinity This is a topic that we already covered, but we will look at it from a ...
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3-3 Oblique Asymptotes What? Oblique? I think that word was on my vocab last month . OK to review for just a minute If a VA cancels out, graph the point as a hole.
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Infinite Limits and Limits to Infinity: Horizontal and Vertical Asymptotes Recall The notation tells us how the limit fails to exist by denoting the ...
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Instead, you possibly get a slant asymptote ... the slant asymptote, if it exists. Find at least two values on each side of the vertical asymptotes to put the ...
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Lesson 2-6 Limits at Infinity and Horizontal Asymptotes Objectives Identify and use limits of functions as x approaches either +/- Identify horizontal asymptotes ...
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Cusp. Again, consider a function continuous at P(c, f(c)) A cusp exists when. are both infinite and. opposite in sign. 15. Assignment. Lesson 4.4 ...
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With rational functions, the vertical asymptotes will be precisely when the denominator is zero. ... The line y=L is a horizontal asymptote of the function f if ...
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The line y = L is called a horizontal asymptote of the ... that the lines. are vertical asymptotes. of the graph of tan. HORIZONTAL ASYMPTOTES. 4. Definition ...
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Slant asymptotes ... To find the equation of slant asymptote, use long division to divide numerator ... asymptote or Slant asymptote. Additional points ...
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Ch 6.7 Graphing Other Trig Functions y = cscx Period: Domain: Range: Asymptotes: y = 1: y = -1: y = secx Period: Domain: Range: Asymptotes: y = 1: y ...
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Rational Functions/Factoring J PAR Y! M th J PAR Y! Vertical Asymptotes Y-intercepts of Rational Functions Horizontal Asymptotes Domain of Rational Functions
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Today in Precalculus Go over homework Notes: Limits with infinity and Asymptotes Homework Limits and asymptotes Infinity as the limit Infinity as the limit ...
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No vertical asymptotes H.A.: y = 3 Guided Practice Find the horizontal and vertical asymptotes of the given function. Use limits to describe the corresponding behavior.
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ASYMPTOTES HORIZONTAL Recall from Section 2.6 that, ... Use the guidelines to sketch the curve A. The domain is: {x | x2 1 0} = {x ...
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Has 2 branches and 2 asymptotes. The asymptotes contain the diagonals of a rectangle centered at the hyperbolas center ... Asymptotes ...
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Determine the vertical asymptotes (if any) of a rational function. ... vertical asymptotes, and horizontal asymptotes for ... Find the slant asymptote for ...
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Cannot have asymptotes. An alternative is fractional polynomials ... Can have asymptote. Non-monotonic (single maximum or minimum) Single turning-point ...
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5-Minute Check on Activity 5-4 Determine the domain, range and horizontal asymptotes for: y = 4x domain: range: HA:
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... and Horizontal asymptotes. Differentiability. First and ... Sketch the graphs and label intercepts, relative extrema, points of inflection and asymptotes. ...
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Today in Pre-Calculus Go over homework. Notes: Asymptotes and End Behavior Need a calculator Homework Unbounded Bounded below b=0 Bounded below b = 1 Unbounded ...
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Cannot have asymptotes. Fractional polynomial models. Describe for one ... Can have asymptote. Non-monotonic (single maximum or minimum) Single turning-point ...
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Sullivan Algebra and Trigonometry: Section 4.3 Rational Functions I Objectives Find the Domain of a Rational Function Determine the Vertical Asymptotes of a Rational ...
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... Asymptote ... all holes and vertical asymptotes in each graph. Horizontal Asymptote ... Identify all excluded values, asymptotes, and holes in. the graph of a ...
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Example: Sketch the graph of, (continued) Second, find the asymptotes. ... Rational Functions: Sketching Graphs. END OF PRESENTATION. Click to rerun the show. ...
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The line y = b is a horizontal asymptote of the graph of a function f if either. Curve Sketching ... Horizontal Asymptotes. Vertical Asymptotes. Example ...
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Asymptotes. Relative Extrema: Determine the critical points: Evaluate sample points: ... Horizontal Asymptotes: Horizontal Asymptote at y=0. Thank You! ...
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C7 Asymptotes of Rational and Other Functions IB Math HL/SL - Santowski (A) Introduction To help make sense of any of the following discussions, graph all ...
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Excluded Values are the vertical asymptotes. Horizontal asymptotes are found in the value table ... B. Steps for multiplication. Factor all polynomials. Cross ...
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... 8 p.91/1, 6, 8, 9, 15, 16, 17, 18, 19, 20, *39,*41. Functions and Asymptotes. 3 ... function as x approaches infinity is the value of the horizontal asymptote. ...
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... infinity, the function approaches the x-axis (the x-axis is an asymptote) ... the domain, range, intercepts, asymptotes, increasing or decreasing function. ...
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Objectives for Section 12.4 Curve Sketching Techniques The student will modify his/her graphing strategy by including information about asymptotes.
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Limits and Asymptotes. Limits can be used to determine vertical and horizontal asymptotes. ... then the function has a vertical asymptote at x = a. If ...
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Since the domain is , and the vertical asymptotes are x = 2, -1, that means that ... Horizontal asymptotes describe the behavior at the ends of a function. ...
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Why exponential functions have horizontal asymptotes ... The horizontal line Q = 0, the t-axis is a horizontal asymptote for the graph of ...
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Most Rational Functions have a vertical asymptote. ... Determine the equations of any vertical asymptotes and the values of x for any ...
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... equations of horizontal asymptotes. The function will have horizontal asymptotes if the degree ... This rational function may have a slant asymptote. 3.4 Notes ...
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... finish early, you may read about asymptotes and work on the remaining problems. We will discuss the significance of horizontal and vertical asymptotes as a class ...
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State the domain, range, any asymptotes, and the transformations of ... D: (- , ) R: (-2, ) Horizontal Asymptote y = -2. Shifts left one unit and down two units. ...
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Vertical Asymptotes: ... To find the horizontal asymptotes, identify the degree of the function (the ... This line is called a slant or oblique asymptote. ...
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Domain Range Vertical Asymptote. y = log3 (-x 3) y = log3 (-(x 3) ... Domain Range Vertical Asymptote ... Identify any asymptotes of the function. ...
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In like manner, we define Limx- cF(x) = - . Vertical Asymptotes ... right, we say that the line x = c is a vertical asymptote of the graph of F(x) Vertical Asymptotes ...
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Must watch Asymptotes (undefined ?) Use Algebra. Sketch in pieces. HW: pg 206 #10,14,17,19, 21,22 ... HW: pg 261 #1-5 DRAW The TRIANGLES for Help. 11/1/06 Wed. TPC ...
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How to sketch graphs of rational functions that have slant asymptotes ... Asymptotes. Vertical. at zeros of the denominator. Horizontal. N D asymptote at y = 0 ...
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Asymptote Slopes: Writing in Standard Form ... Graph the asymptotes (start at the center and use 'Rise over Run') Draw 'U' shapes that go through the vertices ...
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EXAMPLE 1. Graph a rational function of the form y = a. x. Graph ... Draw the asymptotes x ... Draw the branches of the hyperbola so that they pass through the ...
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Conic Sections. Hyperbolas (Day 2) Equations of the Asymptotes. For a hyperbola that opens left and right... For a hyperbola that opens up and down...
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Draw a vertical asymptote at x = 3. Plot the points that are the same for both. ... there are no vertical asymptotes for. Since f(x) is always positive, is ...
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In the diagram below, y = cos x is drawn in gray while y = tan x is drawn in black. ... asymptotes (indicated by broken lines) everywhere the cosine graph ...
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If n = m, the line is a horizontal asymptote. If n m, the graph of f has no horizontal asymptote. Oblique (slant) asymptotes are treated separately. ...
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Domain and range are restricted (denominators may not equal zero.) Basic graph is a hyperbola. Graphs of rational functions may have boundary lines called asymptotes ...
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A hyperbola is a set of points in a plane the difference of whose distances from ... Draw the asymptotes as dotted lines that pass diagonally through the rectangle. ...
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