Modelling Water What can you tell me about this curve?

Slides:

Advertisements

Similar presentations

Transforming graphs of functions

Advertisements

9.3 Rational Functions and Their Graphs

Functions of Several Variables. Constructing Functions of Several Variables The temperature at points in the xy-plane is proportional to the square of.

5.3 Graphs of Rational Functions

Continuity When Will It End. For functions that are "normal" enough, we know immediately whether or not they are continuous at a given point. Nevertheless,

Pre Calculus Functions and Graphs. Functions A function is a relation where each element of the domain is paired with exactly one element of the range.

Precalculus Lesson 2.6 – Lesson 2.7 Rational Functions, Asymptotes

Drawing Straight Line Graphs

3.8 Simplify Rational ExpressionsVocabulary An expression that can be written as a ratio of two polynomials. Rational Expression A number that makes a.

Section 9.2/9.3 Rational Functions, Asymptotes, Holes.

Lesson 2.6 Rational Functions and Asymptotes. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:

Rational Functions A function of the form where p(x) and q(x) are polynomial functions and q(x) ≠ 0. Examples: (MCC9-12.F.IF.7d)

Midterm Review Calculus. UNIT 0 Page  3 Determine whether is rational or irrational. Determine whether the given value of x satisfies the inequality:

Graphing Gas Behavior.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2-4) Then/Now New Vocabulary Key Concept:Vertical and Horizontal Asymptotes Example 1:Find Vertical.

Graphs and Equations in Physics. Label each axis with 1) Quantity Position Time (m) (s) Mass Volume (kg) (mL) ) Units3) Scale.

Graphing Rational Functions. What is a rational function? or.

Density Graph Rules of Construction. Density Graphing Rules  First, look at all your values for mass and volume.  Next, decide on a scale that best.

Lesson 8-3: Graphing Rational Functions

Rational Functions and their Graphs. Definition Rational Function A rational function f(x) is a function that can be written as where P(x) and Q(x) are.

1 Limits and Continuity. 2 Intro to Continuity As we have seen some graphs have holes in them, some have breaks and some have other irregularities. We.

Functions (Section 1-2) Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range.

Lesson 21 Finding holes and asymptotes Lesson 21 February 21, 2013.

Holt McDougal Algebra 2 Multiplying and Dividing Rational Expressions Multiplying and Dividing Rational Expressions Holt Algebra 2Holt McDougal Algebra.

Math PolynomialsTrig Functions Exponential Functions Log FunctionsLogistic Functions Most functions that are encountered in the real world are.

Nuffield Free-Standing Mathematics Activity

Solving Linear Systems by Substitution

Paper for notes Graph paper Pearson 8.3 Graphing Calc.

Graphs and Applications of Linear Equations

2.1Intercepts;Symmetry;Graphing Key Equations

Science Skills Chapter 1.

Summarize the Rational Function Task

Graphing Rational Functions

8.2 Rational Functions and Their Graphs

Rational Functions Algebra

EXAMPLE 1 Find excluded values

Quadratic and Other Nonlinear Inequalities

DENSITY DENSITY = MASS (REFERENCE TABLE) VOLUME

Graphs of Equations In Two Variables; Intercepts; Symmetry

Equations with Rational Expressions and Graphs

$$$ DEAL OR NO DEAL $$$.

الموائع Fluids.

Other Types of Polar Graphs…

Which do you think would have the greater volume and mass? Why?

Summarize the Rational Function Task

A. 4 positive zeros; 1 negative zero

Section 7.1 – Rational Expressions

Safety and Density.

Physics Revision- CHAPTER 3 – Particle model of matter

Notes Over 8.3 Simplifying Natural Base Expressions

Domain, Range, Vertical Asymptotes and Horizontal Asymptotes

Section P.5 – Rational Expressions

Graphs and Polar Equations

Chapter 4 Review.

Section 8.4 – Graphing Rational Functions

Graphing Key Equations

Example 5A: Solving Simple Rational Equations

Unit 1 Notes: Graphing & Density

GCSE Statistics Time Series.

Graphing rational functions

Is it proportional? We will look at some equations, graphs and tables and you will decide if the relationship is proportional. Tell why or why not. If.

More Definite Integrals

7th Grade Eureka Mathematics Week #2

What’s the same and what’s different?

2.5 Basic Differentiation Properties

Presentation transcript:

Modelling Water What can you tell me about this curve? This equation models the volume of 1 kg of water as temperature changes. What can you tell me about this curve?

The Data How can we decide accuracy? What is important to consider? What scale should we use?

The Graph Why is the x axis temperature? What is missing from this graph? What would an examiner be looking for?

The Graph: Analysis Is this graph what you expected? If you saw this graph what equation would you expect created it? What is the minimum point? Given its real life context, does this surprise you?

Density and Ice How is density and volume related? Given that we use 1kg of water, what does that mean? What is going on at 0? Given its real life context, does this surprise you?

Point of Discontinuity A function is said to have a point of discontinuity at x = a or the graph of the function has a hole at x = a, if the original function is undefined for x = a, whereas the related rational expression of the function in simplest form is defined for x = a.

Why?