Curve Sketching Flip Book

Grade-12 MCV4U

Curve Sketching Flip Book Assignment

TEACHER: RUPINDER KAUR

BY: JASKARAN GREWAL

My Rational Function:

WHAT IS A RATIONAL FUNCTION

A rational function is defined as a polynomial divided by a polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the denominator's zeros.

What Is A Y And X-Intercepts.

The x-intercepts are locations on a function or equation's graph that cross or "contact" the xaxis of the Cartesian Plane. Consider this a point with a y-value of zero. The y-intercepts are locations on a function or equation's graph that cross or "contact" the y-axis of the Cartesian Plane. Consider this a point with an x-value of zero.

My X And Y-Intercepts

For y - intercept, we equate the function to 0 which then equals to 1 = 0 , this is a trivial answer which means the function has no y - intercept For xintercept, we substitute 0 for x. y = 1/0-0 = undefined (that also means that the function has no xintercept)

What Are Horizontal, Vertical and Slant Asymptotes.

HORIZONTAL ASYMPTOTE

A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞ . .

VERTICAL ASYMPTOTE

A vertical asymptote of a graph is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

SLANT ASYMPTOTE

A slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞ .

My Slant,Vertical And Horizontal Asymptote

Horizontal asymptote: for this asymptote, we divide the leading terms from both the numerator and the denominator. Therefore we get 1/x^3. This is undefined at x = 0. Hence the horizontal asymptote is y = 0 Vertical asymptote: for this asymptote, we equate the denominator by 0 and then solve for the value of x. X^3 - X= 0 x(x^2 -1) = 0, from this x = 0 Solving the expression in the bracket for the other roots x^2- 1 = 0 x = 1 x = +/- 1 Hence the vertical asymptote is at x = -1, 0, and 1. Slant asymptote: the function has no slant asymptote. Note that we cannot have both horizontal and slant asymptote in one function. We either get slant asymptote or horizontal asymptote.

What is End Behaviour My End Behaviours

End behaviour of a function f describes the behaviour of the function's graph at the "ends" of the x-axis. In other words, the end behaviour of a function describes the graph's trend when we look to the right end of the x-axis(as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Critical Point

Points on the graph of a function where the derivative is zero or does not exist are important to consider in many derivative application problems. If x is in the domain of the function and either f′(x) = 0 or f′(x) does not exist, the point (x, f(x)) is called a critical point of f(x).

Point Of Inflection

The point of inflection, also known as the inflection point, is the point at which the function's concavity changes. It denotes a change in function from concave down to concave up or vice versa.

NOTE FOR MY POINT OF INFLECTION

this equation has no root which means it has no point of inflection. Note: for this particular function, sign chart, slope chart and concavity chart are not applicable.

Concavity

CONCAVITY

The concavity of a function's graph refers to the curvature of the graph over an interval; this curvature can be concave up or concave down. A concave up curve has a shape similar to "U" and a concave down curve has a shape similar to "∩" .

Sketching My Functions Graph

THE END.

INNOCENT HEARTS SECONDARY SCHOOL

Grade-12

MCV4U

Curve Sketching Flip Book Assignment

Student’s Name:

Date of submission:

K/U: /10 T: /10 A: /10 C: /10

This evaluation covered the following expectations: B1.1, B1.2, B1.3, B1.4, and B1.5

Task:

Part 1: Create a foldable flip book by using any rational function and inspect the following elements in a flipbook:

 x and y-intercepts

 Horizontal, vertical and slant asymptotes (including end behaviour)

 Critical points and slop chart

 Point of inflection and concavity chart

 Sketch the function on graph paper with properly labelled axes

Part II: The student has to present it in front of the class.

Directions to make Flip book foldable:

 A title page must include the title of your topic, course code, your name, date of submission, your teacher’s name.

 A graph of the function should be sketch on the graph paper or use Desmos

 You can use these free online digital flipbook websites: flipsnack.com, dcatalog.com etc. for digital flipbook.

 Rubric is attached. You must attach this sheet and rubric with your submission.

 Use proper units and significant digits.

 Use a calculator, the formula sheet, text books/reference material to complete this assignment.

 Do not use self-developed short form notations.

 Plagiarism is not acceptable.

Knowledge/ Understanding (K)

Planning& processingskills (T)

(Observation)

Demonstrates thorough understandingofconcepts

Demonstrates considerable understandingofconcepts

Demonstrates some understandingofconcepts

Demonstrates limited understanding of concepts

-Uses planning skills in selecting function and resources to organize and analysis the concepts accuratelywithahighdegree ofeffectiveness

-usespropertoolstoexplain the concepts and making arguments to interpret the contextwithahighdegreeof effectiveness

-Usesavarietyofsourcesin reachingaccurateconclusions with a high degree of effectiveness

-Uses planning skills in selecting strategies and resources to organize and analysis the concepts accurately with considerableeffectiveness

-usespropertoolstoexplain the concepts and making argumentstointerpret the context with considerable effectiveness

-Usesavarietyofsourcesin reaching conclusions with considerableeffectiveness

-Uses planning skills in selecting strategies and resources to organize and analysis the concepts accurately with some effectiveness

-usespropertoolstoexplain the concepts and making argumentstointerpretthe context with some effectiveness

-Usesavarietyofsourcesin reaching conclusions with someeffectiveness

-Uses planning skills in selecting strategies and resourcestoorganizeand analysis the concepts accurately with limited effectiveness

-uses proper tools to explaintheconceptsand making arguments to interpretthecontextwith limitedeffectiveness

-Usesavarietyofsources inreachingconclusions withlimitedeffectiveness

Making Connection within similar and/or different context

(A) (Observation)

Organization and expression of ideas andinformation

(C)

-Applies conceptual knowledge and skills in familiarcontextswithahigh degreeofeffectiveness

-Makesconnectionsbetween concepts and real world outsidetheclassroomwitha highdegreeofeffectiveness

-expresses and organizes of ideas in diagrams, flipbook etc. logically with a high degreeofeffectiveness

- uses mathematical symbols, formulae, labels, conventionsandterminology with a high degree of effectiveness -communicatesfordifferent audience and purposes in oral andvisualformswitha highdegreeofeffectiveness

-Applies conceptual knowledge and skills in familiar contexts with considerableeffectiveness

-Makes connections betweenconceptsandreal worldoutsidetheclassroom with considerable effectiveness

-expressesandorganizesof ideasindiagrams, flipbook etc. logically with considerable effectiveness

- uses mathematical symbols, formulae labels, conventions and terminology with considerable degree of effectiveness - communicates for different audience and purposesinoral andvisual forms with considerable effectiveness

-Applies conceptual knowledge and skills in familiarcontextswithsome effectiveness

-Applies conceptual knowledge and skills in familiar contexts with limitedeffectiveness

-Makes connections betweenconceptsandreal worldoutsidetheclassroom withsomeeffectiveness

-expressesandorganizesof ideas in diagrams, models, charts etc. logically with someeffectiveness

- uses mathematical symbols, formulae labels, conventions and terminology with some effectiveness

- communicates for different audience and purposesinoralandvisual forms with some effectiveness

- Makes connections between concepts and real world outside the classroom with limited effectiveness

-expresses and organizes of ideas in diagrams, models, charts etc. logically with limited effectiveness -uses mathematical symbols,formulaelabels, conventions and terminology withlimited effectiveness - communicates for different audience and purposesinoralandvisual forms with limited effectiveness