Question

Piecewise function help!!?

Answer 1

http://gyazo.com/5a0be0f54375e895c1c46c4325fc0159

Answer 2

^^ question is in link

Answer 3

-4 and 4 are not equal to 1, use the top rule

Answer 4

1 is equal to 1, so \(f(1)=2\)

Answer 5

im still so confused, i do not remember learning this

Answer 6

lol maybe you are supposed to be learning this now! it is not like you are born knowing it

Answer 7

the way you read the function is this
\(f(x)=\frac{1}{2}x+2\) if x is not equal to 1
so for any number not equal to 1, use that rule
for example
\[f(4)=\frac{1}{2}\times 4+2=2+2=4\]

Answer 8

\[f(-4)=\frac{1}{2}\times (-4)+2\] etc

Answer 9

the only time you do not use that rule is if \(x=1\) because you are told that \(f(1)=2\)

Answer 10

so for my answer for f(-4) i need to do 1/2 x(-4)+2??

Answer 11

yes exactly

Answer 12

and as for the rest im not to sure, its like overwhelming looking at it lol

Answer 13

there is no rest
you are only asked for three numbers
\[f(-4)\] which you know how to compute
\[f(1)\] which you are told is \(2\) and
\[f(4)\] which we already computed

Answer 14

so f(1)= 1/2 (-1)+2?

Answer 15

wait no, f(1)=1/2 (2)+2?

Answer 16

lets go slow

Answer 17

you see on the bottom row, it says " 2 if x = 1" right?

Answer 18

yes

Answer 19

that is another way of saying \[f(1)=2\] i.e. it is 2 if x is 1

Answer 20

so do i just plug it in like the equation we did for -4??

Answer 21

no you do not
you say \(f(1)=2\))

Answer 22

oh okay

Answer 23

any other number you would plug in, but not 1

Answer 24

so f(-4) =0 f(1)=2 f(4)=4?

Answer 25

i got this one thanks. the next one looks more complicated though lol

Answer 26

post it i can help

Answer 27

http://gyazo.com/35cb71d59b6a6a71ae2af3c9e3204d15


^^ okay here it is @satellite73

Answer 28

yeah it is more complicated, but it is not complicated if you know how to read it
for \(f(-2)\) yhou have to figure out which rule to use out of a possible 4
it could be -2,-1,0 or 1

Answer 29

the question is, which one, and you do that be figuring out which inequality \(-2\) satisfies (fits)

Answer 30

evidently it fits the top inequality \(-2\leq x<-1\) so use the top one, i.e.
\[f(-2)=-2\]

Answer 31

of the four posslbe numbers, what do you think \(f(-1.75)\) is? which inequality does \(-1.75\) satisfy ?

Answer 32

the third one? 0?

Answer 33

hmm no

Answer 34

\[0\leq -1.75<1\]is defintely not true

Answer 35

oops i forgot the negative part!

Answer 36

lol yeah that minus sign if for real
try again?

Answer 37

i think the second one -1 but isnt -1 bigger then -1.75? :c

Answer 38

yes -1 is bigger, so no, not the second one

Answer 39

all thats left is 1

Answer 40

unless u can reuse the top equation..

Answer 41

yea
\[-2\leq -1.75<-1\] is true

Answer 42

of course you can reuse it
you did not use it up

Answer 43

oh gosh i feel dumb now lol i thought it was done cuz we already plugged it in ok

Answer 44

so that makes
\[f(-1.75)=2\] use the top one

Answer 45

one more to go, i bet you can do it

Answer 46

1 the last one

Answer 47

oops typo

Answer 48

i meant
\[f(-1.75)=-2\] sorry

Answer 49

yeah you are right,
\[f(1)=1\]

Answer 50

not so hard once you know how to read it right?

Answer 51

woohoo! thanks! i only have 1 more of these questions to go

Answer 52

still want help or you got it?

Answer 53

might need a litle help

Answer 54

kk

Answer 55

I wish there was a way to give you like 10 million medals! lol

Answer 56

http://gyazo.com/e18648acb9277fe638038ae9c3d7b9a9

Answer 57

for the first one is it -1/2*(1)+2??

Answer 58

no

Answer 59

oh man:/ ookay ya i need help

Answer 60

which inequality does 1 satisfy ?

Answer 61

top, middle or bottom?

Answer 62

middle

Answer 63

yes
replace \(x\) by \(1\) in the middle formula, you can do it in your head

Answer 64

1

Answer 65

g(1)=1?

Answer 66

hmmm no

Answer 67

\[g(1)\] use the middle rule
\[f(x)=-(x-1)^2+3\]

Answer 68

not to be mean, but where did you get the one from?
you need
\[g(1)=-(1-1)^2+3\] which is not one for sure

Answer 69

i honestly have no idea im tired, its 3?

Answer 70

yeah 3

Answer 71

and then for the next one it fits best in the middle one agIN I believe

Answer 72

let me look again

Answer 73

yes you are right

Answer 74

so 2?

Answer 75

and thee last one goes in the bottm inequilty so it equals 4? ?

Answer 76

yes 2

Answer 77

yes 4 for the last one

Answer 78

yay thank you so much!

Answer 79

yw hope you learned something even though you did not know it before

Answer 80

i did your a good teacher lol

Answer 81

thanks!