Alicia is writing the program for a video game. For one part of the game she uses the rule (x,y) -->(x- 3, y+4) to move points on the screen. (a) What output does the rule give when the input is ? Show your work. (b) What output does the rule give when the input is ? Show your work. (c) Is the rule a function? Explain why it is or why it is not.

Hey! I can help you :) so lets start with part a. but first, can you tell me the rest of the question please? (a) What output does the rule give when the input is `_____` ? whats supposed to be in that blank spot?

Thank you so much, sorry I didn't realize it cut it out. (6,0) is what would be in the blank spot.

alright, so do you agree that `6` is the `x` value and `0` is the `y` value? if so, we can plug in those numbers in the rule... ( `6` - 3, `0` + 4 ) to make this a little easier... what is `6 - 3`? and what is `0 + 4`?

Yeah, I agree. 6-3=3 and 4+0=4

Correct, so 3 would our new `x-value` and 4 would be out new `y-value` so, `(3,4)`

now we have finished part a :) how about part b, whats supposed to be in the blank?

Wow, thank you again, so much. (3,-4) is what would be in the second blank

alright, so we basically do the same thing since we are using the same rule... (x- 3, y+4) becomes... ( `3` - 3, `-4` + 4) 3 - 3 = ? -4 + 4 = ? Remember to be aware of the signs!!

3-3=0 and -4-4= either 4 or 0?

Oops it's a plus, sorry would it be 4?

subtracting negative numbers can be hard but lemme explain it easier ðŸ˜… `-4 + 4` is the same as doing `4 - 4` do you understand?

is that confusing..?

It would be 0

yup, it would be 0 :) (0,0) would be the output. lets go on to part c now.. do you think this rule is a function?

I think so

you're right, this is considered a function because the points have changed places (or in math terms, shifted). We can use part A as an example. The original point was (6,0) but after be used the rule, the point shifted to (3,4). The point shifts to the left 3 times (hence -3) and goes up 4 (+4) according to the rule.

Ohhhh, okay!

Thank you so much for all your help, I understand it so much better now.

no problem!! my pleasure :)

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