Focus Plan: Function Conjunction

PowerPoint Presentation

Focus Activity and Instruction

They say…A picture is worth a thousand words

Is it?

Which means more?

USA Today reports: A heavy battle took place between the U.S.

Army's 7th Cavalry Regiment and Iraqi forces on March 25, 2003 near the village of Al Faysaliyah, Iraq. A number of civilians, including children, were injured.

Or this…

Retrieved from: http://www.usatoday.com/news/world/iraq/2003-07-06-photo-boy_x.htm

This? April 16, 2007

A gunman kills 32 people in a dorm and a classroom building at Virginia Tech in Blacksburg, Va. The suspect then dies by gunshot himself.

Or This?

Retrieved from http://www.time.com/time/photoessays

In Math, as in life Pictures often mean more than words

The following slides will give you information about the number of high school dropouts there were in the U.S. between 1995 and 2001

TABLE

Bar Graph

Which representation of the data was easier to interpret?

The Table?

Or the Graph?

Classroom Instruction TAKS Objective 2: The student will

demonstrate an understanding of the properties and attributes of functions.

TEK A. 1 (D) Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities

Graph: A picture which represents a relationship (usually functional)

For most people, a graph or diagram is easier to comprehend than a chart with words & numbers

In math

We must be able to represent relationships in many ways

Today we will study –representing math relationships

Meaning…

Can you take a functional relationship and represent it with a:

table model graph

diagram equation inequality

description mapping

Lets Practice With some TAKS questions

The function f(x) = {(1, 2), (2, 4), (3, 6), (4, 8)}

Can be represented in several other ways. Which is NOT a correct representation of the function f(x)?

H x is a natural number less than 5 and y is twice x

J y = 2x and the domain is {1, 2, 3, 4}

9th Grade 9 TAKS

Which Inequality best describes the graph below?

A y > -¾ x + 5

B y < -4/3 x + 5

C y < - ¾ x + 5

D y > -4/3 x + 5

Grade 9 TAKS

Which inequality best describes the graph shown below?

F y ≥ -2x

G y ≥ -x – 2

H y ≥ -2x – 2

J y ≥ x – 2

Grade 10 TAKS

Which mapping best represents the function y = 2x2 + 1 when the replacement set for x is {-1, 0, 3}?

Grade 10 TAKS

Which data set is best described by the function y = -2x2 + 5x?

Grade 10 TAKS

Which quadratic equation best represents the parabola shown below?

A y = x2 + x + 5

B y = x2 + 5

C y = -x2 + 5

D y = -x2 + x + 5

Exit Level TAKS

Represent the following LIST of ordered pairs as a Table: {(-1, -4), (0, -1), (3, 8), (5, 14), …}

x y

-1 -4

0 -1

3 8

5 14

… …

Represent the following LIST of ordered pairs as a Mapping: {(-1, -4), (0, -1), (3, 8), (5, 14)}

Represent the following LIST of ordered pairs as a Verbal Description:

{(-1, -4), (0, -1), (3, 8), (5, 14)…}

The y-values for a set of points are 1 less than 3 times the corresponding

x-values

Represent the following LIST of ordered pairs as an Equation:

{(-1, -4), (0, -1), (3, 8), (5, 14)…}

y = 3x - 1

Represent the following LIST of ordered pairs in Functional Notation:

{(-1, -4), (0, -1), (3, 8), (5, 14)…}

f(x) = 3x - 1

Represent the following LIST of ordered pairs as a graph:

{(-1, -4), (0, -1), (3, 8), (5, 14)…}

You must know how --

To represent functions in many ways and

To determine whether two different representations of a function are equivalent