Question

Which rule is represented by the graph?
2 if x <_ -1
2x if x _> -2

2 if x <_ -2
-2 if x > -2

2 if x < -1
2x if x _> -1

2 if x < -1
2x if x > 2

Answer 1

what is the equation of the left piece?

Answer 2

What do you mean?

Answer 3

the flat horizontal portion

if it were extended in both directions infinitely, what is the equation of that line?

Answer 4

I have no clue.

Answer 5

what's the y coordinate of each point on that line?

Answer 6

-1

Answer 7

the y coordinate is like the height

Answer 8

how high off the "ground" (ie x axis) is this line?

Answer 9

-2 and 2

Answer 10

only focus on the flat horizontal line for now

Answer 11

2

Answer 12

so the equation of that horizontal piece is y = 2

Answer 13

it's only graphed when x < -1

so that's the restriction on that piece

Answer 14

what is the equation of that other piece?

Answer 15

y = -2

Answer 16

hint: it's a linear equation that goes through (0,0) and (1,2)

Answer 17

2x if x > 2?

Answer 18

it's y = 2x

but the restriction is off

Answer 19

_> -1?

Answer 20

much better

Answer 21

so the answer is
2 if x < -1
2x if x _> -1

Answer 22

exactly

Answer 23

it says that you graph y = 2 only if x < -1 or you graph y = 2x if x >= -1

Answer 24

You should be my math teacher haha thank you!

Answer 25

you're welcome, I'm glad I helped out