Question

Here is the function table worksheet: I am confused on some of the parts and it's on a word document, so I hope you can read it.

Answer 1

@ganeshie8 @jim_thompson5910 @Hero @sammixboo @satellite73 the ones that are starred (******) are the ones that I can't do

Answer 2

where you see an \(x\) put an \(m\)

Answer 3

for example
\[f(x)=|x|+3\\
f(m)=|m|+3\]

Answer 4

so is the answer |m| + 3

Answer 5

yes

Answer 6

@satellite73 on #5 what about f(3a) for the function 3x^2 - 2x + 5 for the answer I got 27a^2 - 6a + 5

Answer 7

seems good to me

Answer 8

I mean is that right just asking

Answer 9

yes it is!

Answer 10

@ganeshie8 i wondered who is this black picture holder lol hehe
where is pi lol

Answer 11

lol
\[f(b+2) = |b+2|+3\]

it wont simplify further i think..

Answer 12

yep you can't go any further :P

Answer 13

@ganeshie8 what about 2[|x|] - 5 function

Answer 14

\(\left[[x\right]]\) is the largest `integer` less than or equal to \(x\)

Answer 15

for example :
\(\left[[3.2\right]] = 3\)

because 3 is the largest integer which is still less than 3.2

Answer 16

\(\left[[-3.2\right]] = -4\) for the same reason
-4 is the largest integer less than or equal to -3.2

Answer 17

how would I plug it into my calculator

Answer 18

you dont need calculator for filling in your table

Answer 19

try filling the 2[[x]]-5 column manually

Answer 20

@ganeshie8 this is what I got on Wolfram Alpha: http://www.wolframalpha.com/input/?i=2%5B%5B-5%5D%5D+-5

Answer 21

\[f(-5) = 2[[-5]]-5 \]

-5 is an integer so [[-5]] = -5

plug that in and simplify

Answer 22

@ganeshie8 do that problem as an example to help me better understand it

Answer 23

\[\begin{align}f(-5) &= 2[[-5]]-5 \\~\\&= 2(-5) - 5\\~\\& = -10 -5\\~\\&=-15\end{align}\]


let me see you work f(-1.2)

Answer 24

you need to think of number line
which `integer` comes immediate left of -1.2 ?

Answer 25

f(-1.2) = 2[[-1.2]] - 5
= 2 (-1.2) - 5
= -2.4 - 5
= -7.4

Answer 26

what is largest integer less than -1.2

Answer 27

-1.2

Answer 28

oh what he did with -5 i different
[(-5)]=-5 since -5 is integer itself
greatest integer function is producing the largest integer less than or equal to x

Answer 29

-1

Answer 30

the largest integer less than -1.2 would be -2 don't you agree

Answer 31

yes

Answer 32

2(-2) - 5 right?

Answer 33

no that's not less that -1.2
-1 is greater than -1.2

Answer 34

yes

Answer 35

okay I am confused is it -2 or -1

Answer 36

itis -2 since -2<-1.2

Answer 37

can you do this one now
f(-3.2)=2[(-3.2)]-5

It's -3, so (2*-3) - 5

Answer 38

no not quite
is -3 less than -3.2?

Answer 39

think about an integer less than -3.2

Answer 40

it's -3

Answer 41

no
draw a number line and put those number on it

Answer 42

-3>-3.2 you know

Answer 43

fine it's -4

Answer 44

yes!

Answer 45

okay how about f(-0.2)=2[[-0.2]]-5

Answer 46

now question: For this type of fuction, [[x]], is it always the number less than itself or is it sometimes greater than itself

Answer 47

it is always a number less than x
that's why it is called greatest integer function
look here
http://mathworld.wolfram.com/images/eps-gif/FloorFunction_1000.gif

Answer 48

i know what throws you off
the word "greatest" integer less than or equal
that indicates only that the integer is the largest one that can be less for a value x

Answer 49

so if it's [[0.15]] would it be 1

Answer 50

no again
remember greatest integer "less" than 0.15

Answer 51

see the graph i posted
all the number 0.something
their greatest integer that is less is zero

Answer 52

[[1.3]] try this

Answer 53

let me ask is 1 < 0.15?
think about it, it has to n<x where n is the greatest integer

Answer 54

be*

Answer 55

sorry it would be 0.1 not 1 right

Answer 56

no i said the answer already it is 0

Answer 57

0.1 is not an integer

Answer 58

we are interest in integers (that's why it is called greatest integer function)

Answer 59

interested*

Answer 60

well what's f(0.1) for the greatest integer function of 2[[x]] - 5

Answer 61

f(0.1)=2[[0.1]]-5=2(0)-5=-5

Answer 62

[[0.1]]=0