Question

Piecewise function question

Answer 1

\[f(x) = |x+4| = \left\{\begin{array}{rcc}
x + 4 & \text{if} & x \geq -4 \\
- x - 4& \text{if} & x < -4
\end{array}
\right.
\]

Answer 2

yes i have a graph that i really need help on

Answer 3

could you please hhelp me out

Answer 4

you need to graph something?

Answer 5

no ive got a graph and have some questions about it

Answer 6

ok i can try to help, post the picture

Answer 7

i can post a picture of the worksheet so it'll be easier to see the graph

Answer 8

okay pleasegive me a sec

Answer 9

this is the graph and the first question is f(1)=

Answer 10

and i got 3 as the answer

Answer 11

oh i thought you had to find the function

Answer 12

i do later on

Answer 13

yeah \(f(1)=3\)

Answer 14

and the next one is f(-11)

Answer 15

but on the graph its only till -10

Answer 16

then we better find the function for \(x\leq -5\)

Answer 17

you got the slope right, it is \(\frac{1}{2}\)

Answer 18

yes that is the slope

Answer 19

goes through the point \((-5,3)\) so it is
\[y+5=\frac{1}{2}(x-3)\]

Answer 20

you can plug 11 in to that if you like

Answer 21

oh alright that makes sense

Answer 22

or else write it as
\[y=\frac{1}{2}(x-3)+5\]

Answer 23

is it -2

Answer 24

whoah did i screw that up!!

Answer 25

im not sure haha

Answer 26

slope is \(\frac{1}{2}\) point is \((-5,3)\) equation is
\[y-3=\frac{1}{2}(x+5)\] doe

Answer 27

so its y= 1/2(x+5)+3?

Answer 28

or
\[y=\frac{x}{2}+\frac{11}{2}\]

Answer 29

whatever you like

Answer 30

alright let me solve one sec

Answer 31

cool henna btw

Answer 32

thank you :)

Answer 33

did you get zero yet?

Answer 34

yepp

Answer 35

okay so the next one says find x when f(x)=0

Answer 36

is it 5/2

Answer 37

lol you just did it

Answer 38

im not supposed to use decimals

Answer 39

you found \(f(-11)=0\) right?

Answer 40

yes i did

Answer 41

so that makes "find x when f(x)=0" rather obvious !!

Answer 42

lol idk why i put 5/2

Answer 43

plug in \(-11\) get out zero !!

Answer 44

me neither lol

Answer 45

i got it!

Answer 46

ok next...

Answer 47

alright then lol on to the next one

Answer 48

i have to find the x intercepts

Answer 49

ok we got one right? one is \(-11\)

Answer 50

and i got (5/2,0) and (-11,0)

Answer 51

there is another as well, because it is coming back up at the end and that little arrow indicates it continues up

Answer 52

lets just find the damn function and be done with it k?

Answer 53

lol alright

Answer 54

it actually says to write in point slope form and restricted domain in inequality form

Answer 55

so basically its asking me to write a fuction for each piece

Answer 56

right
so far we are at \[f(x) = \left\{\begin{array}{rcc}
y-3=\frac{1}{2}x+5 & \text{if} & x <-5 \\
3& \text{if} & -5\leq x\leq 1
\end{array}
\right.\]

Answer 57

what is the slope of the next piece? it is a little hard for me to see it

Answer 58

maybe \(-2\)?

Answer 59

you said in the first function theres a 3 ?

Answer 60

under where you write the 5 in the first equation

Answer 61

it is a constant (horizontal line) between -5 and 1 right?

Answer 62

yes thats correct

Answer 63

ooh damn i made a typo there forgot the parentheses

Answer 64

\[f(x) = \left\{\begin{array}{rcc}
y-3=\frac{1}{2}(x+5) & \text{if} & x <-5 \\
3& \text{if} & -5\leq x\leq 1
\end{array}
\right.\]

Answer 65

im a little confused

Answer 66

ok lets go slow and make sure you get it

Answer 67

under the first equation you put a 3

Answer 68

but im not sure why

Answer 69

yeah we are not done
you see how you have 4 long lines in your answer space?

Answer 70

because this piecewise function has four distinct parts

Answer 71

yes i do

Answer 72

4 different lines

Answer 73

okay yes i understand now thank you :)

Answer 74

on the interval from \(-5\) to \(1\) the function is a constant, it is \(f(x)=3\) a horizontal line

Answer 75

yes

Answer 76

so the second line down on the left you should have \(3,-5\leq x\leq 1\) because on that interval it is 3

Answer 77

i understand

Answer 78

oh okay

Answer 79

the next line has slope \(-2\) and goes through \((1,3)\) so its equation is \[y=y-3=-2(x-1)\] in point slope form

Answer 80

would the slope not be a 0?

Answer 81

yes, the slope is zero, the equation is \(y=3\)

Answer 82

okay i got it

Answer 83

okay i got it

Answer 84

\[f(x) = \left\{\begin{array}{rcc}
\frac{1}{2}(x+5)+3 & \text{if} & x <-5 \\
3& \text{if} & -5\leq x\leq 1\\
-2(x-1)+3 &\text{if}&1<x<6
\end{array}
\right.\]

Answer 85

one more to go

Answer 86

okay i got it

Answer 87

last one also has slope \(\frac{1}{2}\) right?

Answer 88

yes it does

Answer 89

and goes through the point \((6,-7\)?

Answer 90

yes i think so

Answer 91

\[f(x) = \left\{\begin{array}{rcc}
\frac{1}{2}(x+5)+3 & \text{if} & x <-5 \\
3& \text{if} & -5\leq x\leq 1\\
-2(x-1)+3 &\text{if}&1<x<6\\
\frac{1}{2}(x-6)-7&\text{if}&x\geq6
\end{array}
\right.\]

Answer 92

that should do it

Answer 93

yes i got it i just have a couple of small questions that i wanted to confirm

Answer 94

ok

Answer 95

are the x intercepts (5/2,0) and (-11,0)?

Answer 96

yes, but there is one more