Question

hi everyone! i have a question......

Answer 1

hello izzy!

Answer 2

and we have it's answer.

Answer 3

^^

Answer 4

Thanks, everyone, glad i got your attention
okay so i have a piecewise fucntion of
\[f(x)=\left\{ x+1, x <-2\right\} and \left\{3x, x \ge -2\right\}\]

how do i find the:
domain
Range
Increasing
decreasing
x intercept
y intercept
continuous
one-to-one
boundedness
Maximum and minimum
And both sides of the end behaviors

ya this is the only homework problem that i am having trouble with, i have tried to look on google, and nothing
i know how to do the absolute value ones and the linear ones, but piece wise are hard becuase they are of different graphing patterns.

Answer 5

hello?

Answer 6

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

Answer 7

ya that's it, i don't know how to do that

Answer 8

domain all real numbers because it is defined for all real numbers

Answer 9

but what is the domain

Answer 10

i know the domain has to do with infinity

Answer 11

domain is anything. all real numbers

Answer 12

no domain just means what possible inputs are there. you can evaluate this at any number

Answer 13

so how would you write that in mathmatical form ?

Answer 14

\[(-\infty, \infty)\] as an interval. maybe that is what you meant by "infinity"

Answer 15

ya! is that the same with range?

Answer 16

range is also all real numbers
\[(-\infty, \infty)\] be

Answer 17

OH

Answer 18

because you see it goes all along the y axis. doesn't skip anything

Answer 19

oh ya that's true

Answer 20

it is always increasing.
it is never decreasing.

Answer 21

well that is not right. it is not increasing at -2

Answer 22

wait why?

Answer 23

isn't the other one going downword tho?

Answer 24

so answer to "increasing" is
\[(-\infty, -2)\cup (2,\infty)\]

Answer 25

not as we read from left to right

Answer 26

oh

Answer 27

increasing / decreasing means as we read from left to right aka as x increases.

Answer 28

so is it as x increases y increases?

Answer 29

otherwise it has no meaning. like asking do the stairs go up or down. depending on which way you are walking! but we walk from right to left

Answer 30

yes, as x increases, so does y

Answer 31

ohhh

Answer 32

x intercept is (0,0)
y intercept is (0,0)
you see it from the picture

Answer 33

it is continuous everywhere except at
\[x=-2\] because it has a jump there

Answer 34

wiat but what about the other one with the +1

Answer 35

it is not one to one because does not pass the horizontal line test

Answer 36

the other one is
\[x+1\] but that is only for
\[x<-2\]

Answer 37

so it never crosses the x - axis or the y - axis. make sure you look at the picture i drew. you can see it from there

Answer 38

OH

Answer 39

okay okay, i get it

Answer 40

it is not bounded, and it has no max or min

Answer 41

what you do when you see these is draw the two pictures, in this case two lines, one to the left and the other to the right

Answer 42

gotta run

Answer 43

okay

Answer 44

thanks