function tables 02/12/12 lntaylor ©. table of contents learning objectives linear equations build a...
TRANSCRIPT
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
Build a Function Table
02/12/12 lntaylor ©
Learning Objectives
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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
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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 = “
02/12/12 lntaylor ©
Previous knowledge
PK 1 Basic Operations and Properties
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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
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Build a Function Table
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Build a Function Table
• 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
TOC02/12/12 lntaylor ©
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)
TOC
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
02/12/12 lntaylor ©
Now you try!
y = 3x - 5
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f(x) = 3x - 5
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)
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
02/12/12 lntaylor ©
Now you try!
y = - 3x - 5
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f(x) = -3x - 5
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
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
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Build a T Chart
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Build a T Chart
• Build a T Chart 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
TOC02/12/12 lntaylor ©
f(x) = 2x + 1
Step 1 – Construct T Chart
Build 2 column Table
Build Heading
Step 2 – Choosing x values
Start with x = 0
Plug 0 into equation
Solve for y
Build x 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)
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
02/12/12 lntaylor ©
Now you try!
y = - x - 5
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f(x) = - x - 5
Step 1 – Construct T Chart
Build 2 column Table
Build Heading
Step 2 – Choosing x values
Start with x = 0
Plug 0 into equation
Solve for y
Build x column
Build y column
Check your work! Did you?
Note that every x has one y
x and y together are called ordered pairs (coordinates and a single point on a graph)
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
02/12/12 lntaylor ©
Reading a Function Table (T Chart)
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Reading a Function Table or a T Chart
• Read a T Chart for f(x)
– You are given certain information in a function 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
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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)
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-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
02/12/12 lntaylor ©
Now you try!
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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 -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
02/12/12 lntaylor ©
Now you try!
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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
-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
02/12/12 lntaylor ©
Graphing from a Function Table
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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
-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
02/12/12 lntaylor ©
Now you try!
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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
Locate coordinate on graph
Find 2nd point
Find 3rd point
Draw line
Label Line
y = 2x
02/12/12 lntaylor ©
Now you try!
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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
Locate coordinate on graph
Find 2nd point
Find 3rd point
Draw line
Label Line
y = - ¾ x
02/12/12 lntaylor ©
Quadratics
Build a Function Table
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Quadratic Equations
• Quadratic Equations f(x) = ax² + bx + c
– You are given certain information in a function f(x)
• 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
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f(x) = x² - 5x - 6
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)
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
02/12/12 lntaylor ©
Now you try!
f(x) = x² + 2x + 1
TOC02/12/12 lntaylor ©
f(x) = x² + 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)
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
02/12/12 lntaylor ©
Now you try!
f(x) = x² - 4
TOC02/12/12 lntaylor ©
f(x) = x² - 4
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)
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
02/12/12 lntaylor ©