Question

Which graph represents the piecewise-defined function?

y={−x+3   if  x<1 2x−4   if  x≥1

A. https://static.k12.com/nextgen_media/assets/8112481-NG_AL1_Quiz_4_11_Pool5_Var2_D.jpg

B. https://static.k12.com/nextgen_media/assets/8112478-NG_AL1_Quiz_4_11_Pool5_Var2_A.jpg

C. https://static.k12.com/nextgen_media/assets/8112480-NG_AL1_Quiz_4_11_Pool5_Var2_C.jpg

D. https://static.k12.com/nextgen_media/assets/8112479-NG_AL1_Quiz_4_11_Pool5_Var2_B.jpg

Answer 1

hint: start by graphing y = -x + 3, and limit your domain to x < 1

Answer 2

would it be an open circle or a closed circle?

Answer 3

open

Answer 4

good, so let's figure out where the open circle would be

Answer 5

if x = 1, y = -x + 3 = ?

Answer 6

x = -y + 3

Answer 7

no, this is not like our other problem, y isn't equal to x anymore

Answer 8

x = 1 tells us that we can replace "x" with "1" whenever x shows up

Answer 9

y = -x + 3

replace "x" with 1, and what does y equal now?

Answer 10

3

Answer 11

try one more time

Answer 12

1

Answer 13

one more time

Answer 14

write down y = -x + 3

Answer 15

-1

Answer 16

erase x and write "1" where x used to be

Answer 17

what do you have now?

Answer 18

-1

Answer 19

take a piece of paper and a pen

Answer 20

write down "y = -x + 3"

Answer 21

erase or cross out the x

Answer 22

then write "1" where x used to be

Answer 23

leave everything else alone.

Answer 24

what do you have now?

Answer 25

y = 1+ 3 =

Answer 26

don't forget the negative sign

Answer 27

it's y = -x + 3

negative x plus 3

Answer 28

after you substitute 1 for x, what do you have now?

Answer 29

i was thinking about that at first with -x

Answer 30

(1, 3)

Answer 31

no

Answer 32

please follow my steps exactly

Answer 33

write down "y = -x + 3"

erase the x (leave the negative sign there" and replace x with 1

Answer 34

what do you have?

Answer 35

y = -x + 3

Answer 36

again, replace the "x" with 1

Answer 37

y = -1 + 3

Answer 38

good, and what does -1 + 3 equal?

Answer 39

2

Answer 40

good, so we have an open circle at (1,2)

Answer 41

which two graphs match this?

Answer 42

D.

Answer 43

B.

Answer 44

ah, yes, d and b.

now, notice that the graph y = -x + 3 has a negative slope

Answer 45

which answer choice has a negative slope on the values x < 1?

Answer 46

B

Answer 47

good so b is our answer

Answer 48

IS IT ?

Answer 49

yes B

Answer 50

thank you a lot appreciate it

Answer 51

sorry for problems and confusion and fraustration

Answer 52

nah, it's ok, if I seem cross it's because today has been a stressful mod day

Answer 53

a lot of people are causing problems in the chat

Answer 54

yeah me 2