Question

Graph each function. Identify the domain and range.
f(x) = {x/3, x < or equal to 0
2x - 6, 0 < x < 2
1, x > or equal to 2

Answer 1

f(x) = {x/3, x < or equal to 0
2x - 6, 0 < x < 2
1, x > or equal to 2


literally means

f(x) = x/3 if x <= 0

OR

f(x) = 2x-6 if 0 < x < 2

OR

f(x) = 1 if x >= 2

Answer 2

To graph this, you graph y = x/3, but you only do so for x values less than or equal to 0.

Then you add on y = 2x-6 but only for x values between 0 and 2 (excluding both 0 and 2)

Finally, you add on y = 1, and you graph this for values of x greater than or equal to 2

Answer 3

@jim_thompson5910 How many lines will be graphed

Answer 4

There are 3 pieces, so 3 lines.

Answer 5

How would they look on a graph

Answer 6

just graph y = x/3

Answer 7

Then erase everything less than x = 0

Answer 8

do the same with the other pieces

Answer 9

Are the lines going to be spread out

Answer 10

@jim_thompson5910 Can you show me all the lines, because I don't get it

Answer 11

one moment please

Answer 12

ok

Answer 13

have a look at this page and tell me if it helps or not

http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-algebra/07-graphing-piecewise-defined-functions-01.htm

Answer 14

it gives a pretty detailed explanation of piecewise functions and how to graph them

Answer 15

really

Answer 16

I can graph 2, but don't know how 3 would look

Answer 17

graph 3 would be a horizontal line at 1 on the y axis

Answer 18

but you're only graphing from x = 2 and to the right

Answer 19

graph 3 would be left of y-axis and right of y - axis

Answer 20

no, just on the right side

Answer 21

from x = 2 and onward to the right

Answer 22

@jim_thompson5910 what's the equations for the 1st and 2nd graph and what is the domain and range???

Answer 23

the equations are the first and second pieces

Answer 24

then use the graph to find the domain

remember the domain is the set of allowed inputs

the range is the set of possible outputs

Answer 25

Range has to be {y/y > 3} for example

Answer 26

look at the graph and see which y values come out, the complete set or list will make up the range

Answer 27

Idk

Answer 28

The domain is all real numbers

Answer 29

yea I got that

Answer 30

it's just the rang

Answer 31

for the range it would probably be easiest to just graph the function and see which y-values are convered

Answer 32

covered

Answer 33

What would the y = mx + b look like for all 3

Answer 34

x/3 = 1/3x+0
2x-6=2x-6
1 = 0x+1 or just a straight, horizontal line from x= 2 to infinity

Answer 35

so the y values must be the same

Answer 36

no, because they all have different domains, their ranges will be different

Answer 37

so how will it work

Answer 38

what am I looking

Answer 39

@ArkGoLucky what am I looking for

Answer 40

sorry was away for a few minutes
so the range of a function is all the outputs of the function, or the y values.
so graph the functions and see the range of the y values and that's your range

Answer 41

I got it already sorry man