Question

Graph the piecewise function.

Answer 1

@peachpi

Answer 2

this one im completely confused on

Answer 3

can you plot
y= 3x -5
?

Answer 4

i dont know what im supposed to do on this problem.

Answer 5

you plot 3 lines
but the lines don't go on forever.

The first step is plot
y= 3x-5

then erase the part where x is bigger than -1
can you do that ?

Answer 6

im confused by what you just said. im sorry

Answer 7

do you know how to plot the line
y= 3x-5

(answer is yes or no)

Answer 8

no

Answer 9

pick a number for x, for example x=-1
then figure out y using
y= 3* -1 -5
can you find y ?

Answer 10

i got y=-8 is that correct?

Answer 11

yes, so we know (-1, -8) is a point on the line

can you plot that point ?

Answer 12

okay i did that whats next

Answer 13

we need one more point, and then we draw a line through the two points

we should try x=-2
can you find y when x= -2, using
y= 3x-5

Answer 14

y= -11

Answer 15

yes ,so another point is (-2, -11)

Answer 16

now what?

Answer 17

next, if we look at what they say

\[ y= 3x -5, \text{ } x\le -1\]
that says the line goes forever toward minus infinity, but it stops at x=-1
and because of the \( \le\) (i.e. the less than or equal)
the line includes the point (-1,-8)
so we put a solid dot at that point.

Answer 18

It should look something like this:

Answer 19

yes thats what i have so far

Answer 20

now we do the next line
y= -2x +3 for -1 < x < 4

we plot that line, but only between x= -1 and x=4

I would find the y value for x=-1
plot that point. (But use an *open circle* to show that the point is not part of the line)
ditto for x=4

can you find those two points ?

Answer 21

(-1,5) and (-4,11)

Answer 22

ok on the first point. but the second one should use x=4 (not -4) (see the original problem)

Answer 23

oh sorry (4,-5)

Answer 24

now plot those 2 points with OPEN circles
because though they are the end points of the line the "less than"
x < 4 means x is not allowed to be 4 (so the point 4,-5 is not part of the line)

Answer 25

It should look like this

Answer 26

okay got that

Answer 27

the last part is
y=2 for x>= 4

that is a horizontal line at y=2
with a SOLID dot at (4,2)
and the line goes to the right forever.

Answer 28

is that it?

Answer 29

yes, it should look like this

Answer 30

ok ?

Answer 31

thank you so much

Answer 32

yw

Answer 33

i gave you a medal