Question

Given the function f(x) = 3(x – 3)^2 + 2, indicate the shifts that will affect the location of the vertex, and explain what effect they will have. Use complete sentences.

f(x+4)
f(x) + 4
f(4x)
4⋅f(x)

Answer 1

@Nurali
@phi

Answer 2

@iGreen

Answer 3

y=f(x)

Answer 4

e f(x)=x

Answer 5

ignore the e on the second answer

Answer 6

, a straight line going through the origin and up and to the right with a slope of 1.

Answer 7

Now let's add 1 to the function:
y=f(x)+1=x+1

Answer 8

Why would we add a 1?

Answer 9

we're changing the function and the graph

Answer 10

Adding a positive value to the result translates the graph in the direction of positive y, and adding a negative value translates in the direction of negative y.

Answer 11

Oh okay. Are we doing the first one? f(x+4) ?

Answer 12

So we're trying to determine if we shift from left or right

Answer 13

yes :)

Answer 14

What is the value of y at x=0? x=1, x=−3?

Answer 15

We shift to the left 4 units. Correct?

Answer 16

Yes! :)

Answer 17

So the first one would be (-1,2) right?

Answer 18

You are indeed correct

Answer 19

Alright I'm kinda getting this now.

For f(x)+4 would be move 4 units horizontally?

Answer 20

Very good :)

Answer 21

Idk how to do f(4x)...lol

Answer 22

ok, let me help

Answer 23

we have y=f(x)=x2. y=f(x+3)+2=(x+3)2+2 and y=f(x+2)−3=(x+2)2−3

Answer 24

y=f(x)+(−1)=f(x)−1

Answer 25

y=f(x)+a
translates the graph along the y axis by a, with a>0 moving the graph in the direction of increasing y values, and a<0 moving the graph in the direction of decreasing y values. What happens if a=0?

Answer 26

Idk... this is kinda confusing now

Answer 27

ok, I'm going to call extra help

Answer 28

If you don't mind

Answer 29

I think we would shift the function to (1,2)

Answer 30

or (3/4 , 2) <---- I think this one is correct

Answer 31

Yes, that is correct

Answer 32

We transform the function to g(x), which would then shift the function to (3/4 , 2)...
Something like that

Answer 33

What about the last one?
My guess is we also transform the function to g(x) like from the third one, then shift the function to (3,8)

Answer 34

Yes

Answer 35

Is that it?

Answer 36

yes

Answer 37

Would you mind helping me with a few more?

Answer 38

sure

Answer 39

just repost the question and tag me

Answer 40

alright

Answer 41

I posted it and tagged you