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

so I believe that in the first it shifts it up, the second shifts it to the right. but I don't understand the last two....

Answer 2

@whpalmer4 can you please help

Answer 3

@ashy98

Answer 4

What happens if we add or subtract something from the result of a function?

Answer 5

I have no clue...

Answer 6

If we have f(x)=x, simple case, a straight line going through the origin and up and to the right with a slope of 1.

Answer 7

so if you add or subtract something it will shift the line up and down?

Answer 8

Now let's add 1 to the function:
y=f(x)+1=x+1
What does our new graph look like? What is the value of y at x=0? x=1, x=−3?

Answer 9

Yes, 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 10

how do we shift right or left?

Answer 11

adding a positive or negative integer with in the parenthesis?

Answer 12

(-3,-3), (-2,-2), (-1, -1), (0,0), (1,1), (2,2), (3,3) that's the first line
(-3,-2), (-2, -1), (-1, 0), (0, 1), (1,2), (2,3), (3,4) that's the second line

Answer 13

oh okay, that makes sense..

Answer 14

adding or subtracting from the argument of the function is to translate the graph to the left or the right.

Answer 15

0kay.. what happens when you multiply or divide from the function?

Answer 16

Do you have a guess?

Answer 17

I honestly didn't know you could before I saw this equation, so I have no clue what it will do to the graph..

Answer 18

you stretch or compress it

Answer 19

what does that mean?

Answer 20

if there is a function y=f(x)
c*f(x) will stretch it vertically and f(x)/c will compress it vertically
f(c*x) will compress it horizontally and f(x/c) will stretch it horizontally

Answer 21

Horizontal Changes

A horizontal stretching is the stretching of the graph away from the y-axis.
A horizontal compression is the squeezing of the graph towards the y-axis.
If the original (parent) function is y = f(x), the horizontal stretching or compressing of the function is given by the function g(x), where g(x) = f(bx).

Answer 22

Vertical Changes

A vertical stretching is the stretching of the graph away from the x-axis.
A vertical compression is the squeezing of the graph towards the x-axis.
If the original (parent) function is y = f(x), the vertical stretching or compressing of the function is given by the function g(x), where g(x) = bf(x).

Answer 23

Does that help?

Answer 24

so does that mean that the slope would change from say 1 to 1/ any number higher?

Answer 25

if 0 < b < 1 (a fraction), the graph is stretched horizontally by a factor
of b units.
if b > 1, the graph is compressed horizontally by a factor of b units.

if b should be negative, the horizontal compression or horizontal stretching of the graph is followed by a reflection of the graph across the y-axis.

Answer 26

oh okay.. im understanding a little better.. so if x is anything greater than one it stretches and anything le than one it will compress?

Answer 27

. It affects where it reflects

Answer 28

Whether or not it is across the y or x axis

Answer 29

for instance in vertical If b should be negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.

Answer 30

ahhh okay hats making a lot more sense to me.

Answer 31

now how does it affect the vertex?

Answer 32

You can see that the vertex moved from (3,2) to (−1,2)

Answer 33

And 3 - (-1)

Answer 34

oh yeah, so it moves the way the graph would?

Answer 35

Yes

Answer 36

So can you solve it from here?

Answer 37

f(x + 4) shifts the function to the left by 4 units,
which results in the vertex shifting from (3,2) to (-1,2).

(ii) f(x) + 4 shifts the function vertically by 4 units,
which results in the vertex shifting to (3,6).

(iii) The transformed function is

g(x) = f(4x) = 3*(4x - 3)^2 + 2 = 48*(x - (3/4))^2 + 2,

so the vertex shifts to ((3/4), 2).

(iv) The transformed function is

g(x) = 4*f(x) = 12*(x - 3)^2 + 8, so the vertex shifts to (3,8)

Answer 38

so the vertex moves the same as the graph , if you do f(x)+1 it move up unless negative, F(x+1) changes it to the right unless negative and multiplying with expand it while dividing will compress it? am I right?

Answer 39

Correct

Answer 40

oh okay thankyou. this has really helped me.

Answer 41

Your welcome!

Answer 42

Think of it this way with multiplication you will get a larger number than dividing

Answer 43

division makes things smaller

Answer 44

that makes it a little easier to understand,

Answer 45

Ok good