5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number...
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![Page 1: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/1.jpg)
![Page 2: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/2.jpg)
5 x2 25
How would you use your calculator to solve 52?
The number you entered is the input number (or x-value on a graph).The result is the output number (or y-value on a graph).The x2 key illustrates the idea of a function.
InputInput OutputOutput
Press:Press:
![Page 3: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/3.jpg)
A function is a relation that gives a single output number for every valid input number.A function is a relation that gives a single
output number for every valid input number.
There are many ways to represent relations:There are many ways to represent relations:
A relation is a rule that produces one or more output numbers for every valid input number.A relation is a rule that produces one or more output numbers for every valid input number.
These are all ways of showing a relationship between two
variables.
These are all ways of showing a relationship between two
variables.
GraphEquationTable of valuesA set of ordered pairsMapping
![Page 4: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/4.jpg)
A function is a rule that gives a single output number for every valid input number.
A function is a rule that gives a single output number for every valid input number.
To help remember & understand the definition:
Think of your input number, usually your x-coordinate, as a letter.Think of your input number, usually your x-coordinate, as a letter.
Think of your output number, usually your y-coordinate, as a mailbox.Think of your output number, usually your y-coordinate, as a mailbox.
![Page 5: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/5.jpg)
A function is a rule that gives a single output number for every valid input number.
A function is a rule that gives a single output number for every valid input number.
Input number Input number
Output number Output number
Can you have one letter going to two different mail boxes?Can you have one letter going to two different mail boxes?
Not a FUNCTIONNot a FUNCTION
![Page 6: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/6.jpg)
A function is a rule that gives a single output number for every valid input number.
A function is a rule that gives a single output number for every valid input number.
Input number Input number
Output number Output number
Can you have two different letters going to one mail box?
Can you have two different letters going to one mail box?
![Page 7: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/7.jpg)
Are these relations or functions?Are these relations or functions?
x y
x y1 52 63 74 6
1
2
3
4
1
2
3
4
5
6
7
5
6
7
Function &
Relation
Function &
Relation
![Page 8: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/8.jpg)
Are these relations or functions?Are these relations or functions?
x y
x y1 52 61 71 6
1
2
1
2
5
6
7
5
6
7
Not a Function but a
Relation
Not a Function but a
Relation
![Page 9: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/9.jpg)
xx yy
x y1 52 62 113 8
1
2
3
1
2
3
5
6
8
11
5
6
8
11
Not a functionBut a relationNot a functionBut a relation
Are these relations or functions?Are these relations or functions?
![Page 10: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/10.jpg)
x y-2 -
1-1 1 0
3 1
5
x y-2 -
1-1 1 0
3 1
5
Double the number and add 3Double the number and add 3
As an equation:
In words:
y = 2x + 3y = 2x + 3
As a table of values:
As a set of ordered pairs:(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3,
9)(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)
These all represent the
SAME function!
These all represent the
SAME function!
![Page 11: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/11.jpg)
Lesson 5.2 (PART 2)
Math 10CMath 10C
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Functional NotationAn equation that is a function may be expressed using functional notation. The notation f(x) (read “f of (x)”) represents the variable y.
![Page 13: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/13.jpg)
Example: y = 2x + 6 can be written as f(x) = 2x + 6.
Given the equation y = 2x + 6, evaluate when x = 3.y = 2(3) + 6 y = 12
Functional Notation Cont’d
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For the function f(x) = 2x + 6, the notation f(3) meansthat the variable x is replaced with the value of 3.
f(x) = 2x + 6f(3) = 2(3) + 6f(3) = 12
Functional Notation Con’t
![Page 15: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/15.jpg)
Given f(x) = 4x + 8, find each:1. f(2)
2. f(a +1)
3. f(4a)
Evaluating Functions
= 4(2) + 8= 16
= 4(a + 1) + 8= 4a + 4 + 8= 4a + 12
= 4(-4a) + 8= -16a+ 8
![Page 16: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/16.jpg)
If f(x) = 3x 1, and g(x) = 5x + 3, find each:
Evaluating More Functions
= [3(2) -1] + [5(3) + 3]= 6 - 1 + 15 + 3= 23
= [3(4) - 1] - [5(-2) + 3]= 11 - (-7)= 18
= 3[3(1) - 1] + 2[5(2) + 3]= 6 + 26= 32
1. f(2) + g(3)
2. f(4) - g(-2)
3. 3f(1) + 2g(2)
![Page 17: 5x2x2 25 How would you use your calculator to solve 5 2 ? The number you entered is the input number (or x-value on a graph). The result is the output.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649da25503460f94a8f020/html5/thumbnails/17.jpg)
5.2 QUESTIONS: MUST BE DONE FOR MONDAY!