function tables 02/12/12 lntaylor ©. table of contents learning objectives linear equations build a...

Function Tables

02/12/12 lntaylor ©

Table of Contents

Learning Objectives

Linear Equations

Build a Function Table

Build a T Chart

Reading a Function Table

Graphing from a Function Table

Quadratic Equations



Learning Objectives

TOC02/12/12 lntaylor ©

Learning Objectives

LO 1

LO 2

Understand what a Function Table represents

Perform basic operations with Function Tables

LO 3 Build ANY Equations from a Function Table


Definitions

Definition 1 A Function Table is a way of expressing a relationship between x and y values

TOC

Definition 2 A T Chart is a Function Table in a different format

Definition 3 A Function states that for every x there is one particular y

Definition 4 f(x) is another way of saying “function” or “y = “


Previous knowledge

PK 1 Basic Operations and Properties


Rule 1

Rule 2

Plug in x = 0 and find y

Go up and down the same amount for each additional x value

Rule 3 Always check your work

Basic Rules of Function Tables



• Build a Function Table for f(x) = 2x + 1

– You are given certain information in a function f(x)

• Given a slope (m) which is the number in front of the x

• Given a y intercept (yi or b) which is the number after the x

• Start with x = 0 and plug it into the equation; find y

• Go up or down the same amount for the next x’s


f(x) = 2x + 1

Step 1 – Construct Table

Build 3 column Table

Build Headings

Step 2 – Choosing x values

Start with x = 0

Plug 0 into equation

Solve for y

Build x column

Build middle column

Build y column

Check your work!

Note that every x has one y

x and y together are called ordered pairs (coordinates and a single point on a graph)

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2x + 1

x f(x) or y

0 2(0) + 1 1

-3

-2

-1

0

1

2

3

2(-3) + 1

2(-2) + 1

2(-1) + 1

2(0) + 1

2(1) + 1

2(2) + 1

2(3) + 1

-5

-3

-1

1

3

5

7


Now you try!

y = 3x - 5


f(x) = 3x - 5



Build Headings


Start with x = 0


Solve for y

Build x column

Build middle column

Build y column

Check your work!



TOC

3x - 5

x f(x) or y

0 3(0) - 5 -5

-3

-2

-1

0

1

2

3

3(-3) - 5

3(-2) - 5

3(-1) - 5

3(0) - 5

3(1) - 5

3(2) - 5

3(3) - 5

-14

-11

-8

-5

-2

1

4


Now you try!

y = - 3x - 5


f(x) = -3x - 5



Build Headings


Start with x = 0


Solve for y

Build x column

Build middle column

Build y column

What is different between the last two equations?

y values are reversed! Why?

The slope sign changed!

TOC

-3x - 5

x f(x) or y

0 3(0) - 5 -5

-3

-2

-1

0

1

2

3

-3(-3) - 5

-3(-2) - 5

-3(-1) - 5

-3(0) - 5

-3(1) - 5

-3(2) - 5

-3(3) - 5

4

1

-2

-5

-8

-11

-14


Build a T Chart


Build a T Chart

• Build a T Chart for f(x) = 2x + 1


• Given a slope (m) which is the number in front of the x

• Given a y intercept (yi or b) which is the number after the x

• Start with x = 0 and plug it into the equation; find y

• Go up or down the same amount for the next x’s


f(x) = 2x + 1

Step 1 – Construct T Chart


Build Heading


Start with x = 0


Solve for y

Build x column

Build y column

Check your work!



TOC

2x + 1

0 1

-3

-2

-1

0

1

2

3

-5

-3

-1

1

3

5

7

x, y

-3, -5

-2, -3

-1, -1

0, 1

1, 3

2, 5

3, 7


Now you try!

y = - x - 5


f(x) = - x - 5

Step 1 – Construct T Chart


Build Heading


Start with x = 0


Solve for y

Build x column

Build y column

Check your work! Did you?



TOC

- x - 5

0 -5

-3

-2

-1

0

1

2

3

-2

-3

-4

-5

-6

-7

-8

x, y

-3, -2

-2, -3

-1, -4

0, -5

1, -6

2, -7

3, -8


Reading a Function Table (T Chart)


Reading a Function Table or a T Chart

• Read a T Chart for f(x)


• Given a Δy – how much each y value changes

• Given a Δx – how much each x value changes

• The slope m is Δy/ Δx

• Given a y intercept (yi or b) which is where x = 0


What is f(x)?

Step 1 – Find Δy

subtract each y value from the one above it

Is it consistent?

Step 2 - Find Δx

Subtract each x value from the one above it

Is it consistent?

Step 3 – find m and b

Slope (m) = Δy/Δx

B or yi intercept where x = 0

Step 4 – write f(x)

TOC

-3 7

-2 5

-1 3

0 1

1 -1

2 -3

3 -5

5 – 7 = – 2

3 – 5 = – 2

1 – 3 = – 2

– 1 – 1 = – 2

– 3 – – 1 = – 2

– 5 – – 3 = – 2

yes

– 2 – – 3 = 1

– 1 – – 2 = 1

0 – – 1 = 1

1 – 0 = 1

2 – 1 = 1

3 – 2 = 1

yes

Δy = – 2xΔx = 1

f(x) = -2x + 1

+ 1


Now you try!


What is f(x)?

Step 1 – Find Δy


Is it consistent?

Step 2 - Find Δx


Is it consistent?


Slope (m) = Δy/Δx



TOC

-3 -4

-2 -2

-1 0

0 2

1 4

2 6

3 8

– 2 – – 4 = 2

0 – – 2 = 2

2 – 0 = 2

4 – 2 = 2

6 – 4 = 2

8 – 6 = 2

yes

– 2 – – 3 = 1

– 1 – – 2 = 1

0 – – 1 = 1

1 – 0 = 1

2 – 1 = 1

3 – 2 = 1

yes

Δy = 2xΔx = 1

f(x) = 2x + 2

+ 2


Now you try!


What is f(x)?

Step 1 – Find Δy


Is it consistent?

Step 2 - Find Δx


Is it consistent?


Slope (m) = Δy/Δx



TOC

-6 5

-4 3

-2 1

0 -1

2 -3

4 -5

6 -7

3 – 5 = – 2

1 – 3 = – 2

– 1 – 1 = – 2

– 3 – – 1 = – 2

– 5 – – 3 = – 2

– 7 – – 5 = – 2

yes

– 4 – – 6 = 2

– 2 – – 4 = 2

0 – – 2 = 2

2 – 0 = 2

4 – 2 = 2

6 – 4 = 2

yes

Δy = - 2xΔx = 2

f(x) = – x – 1

– 1


Graphing from a Function Table


6

5

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5

-1

-2

-3

-4

-5

Graph f(x)

TOC

x y

-6 5

-4 3

-2 1

0 -1

2 -3

4 -5

6 -7

Step 1

Find x = 0

Locate coordinate on graph

Find 2nd point

Find 3rd point

Draw line

Label Line

y = - x - 1


Now you try!


6

5

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5

-1

-2

-3

-4

-5

Graph f(x)

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x y

3 6

2 4

1 2

0 0

-1 -2

-2 -4

-3 -6

Step 1

Find x = 0


Find 2nd point

Find 3rd point

Draw line

Label Line

y = 2x


Now you try!


6

5

4

3

2

1

-5 -4 -3 -2 -1 1 2 3 4 5

-1

-2

-3

-4

-5

Graph f(x)

TOC

x y

-12 9

-8 6

-4 3

0 0

4 -3

8 -6

12 -9

Step 1

Find x = 0


Find 2nd point

Find 3rd point

Draw line

Label Line

y = - ¾ x


Quadratics



Quadratic Equations

• Quadratic Equations f(x) = ax² + bx + c


• Width of the curve is determined by (a)

• Symmetry is determined by (the opposite of b/2a)

• Y intercept of the curve is determined by (c)

• Remember all function tables are the same regardless of the equation

• Go up or down the same amount and look for consistency


f(x) = x² - 5x - 6



Build Headings


Start with x = 0


Solve for y

Build x column

Build middle column

Build y column

Check your work!



TOC

x² - 5x - 6

x f(x) or y

0 0² -5(0) -6 -6

-3

-2

-1

0

1

2

3

(-3)² -5(-3) - 6

(-2)² -5(-2) - 6

(-1)² -5(-1) - 6

(0)² -5(0) - 6

(1)² -5(1) - 6

(2)² -5(2) - 6

(3)² -5(3) - 6

18

8

0

-6

-10

-12

-13


Now you try!

f(x) = x² + 2x + 1


f(x) = x² + 2x + 1



Build Headings


Start with x = 0


Solve for y

Build x column

Build middle column

Build y column

Check your work!



TOC

x² + 2x + 1

x f(x) or y

0 0² + 2(0) +1 1

-3

-2

-1

0

1

2

3

(-3)² + 2(-3) + 1

(-2)² + 2(-2) + 1

(-1)² + 2(-1) + 1

(0)² + 2(0) + 1

(1)² + 2(1) + 1

(2)² + 2(2) + 1

(3)² + 2(3) + 1

4

1

0

1

4

9

16


Now you try!

f(x) = x² - 4


f(x) = x² - 4



Build Headings


Start with x = 0


Solve for y

Build x column

Build middle column

Build y column

Check your work!



TOC

x² - 4

x f(x) or y

0 0² - 4 - 4

-3

-2

-1

0

1

2

3

(-3)² - 4

(-2)² - 4

(-1)² - 4

(0)² - 4

(1)² - 4

(2)² - 4

(3)² - 4

5

0

- 3

- 4

- 3

0

5


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