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)

- anonymous

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- schrodinger

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- anonymous

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....

- anonymous

@whpalmer4 can you please help

- anonymous

@ashy98

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## More answers

- jchick

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

- anonymous

I have no clue...

- jchick

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.

- jchick

##### 1 Attachment

- anonymous

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

- jchick

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?

- jchick

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.

- jchick

how do we shift right or left?

- anonymous

adding a positive or negative integer with in the parenthesis?

- jchick

(-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

- anonymous

oh okay, that makes sense..

- jchick

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

- anonymous

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

- jchick

Do you have a guess?

- anonymous

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

- jchick

you stretch or compress it

- anonymous

what does that mean?

- jchick

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

- jchick

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).

- jchick

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).

- jchick

Does that help?

- anonymous

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

- jchick

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.

- anonymous

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?

- jchick

. It affects where it reflects

- jchick

Whether or not it is across the y or x axis

- jchick

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.

- anonymous

ahhh okay hats making a lot more sense to me.

- anonymous

now how does it affect the vertex?

- jchick

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

- jchick

And 3 - (-1)

- anonymous

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

- jchick

Yes

- jchick

So can you solve it from here?

- jchick

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)

- anonymous

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?

- jchick

Correct

- anonymous

oh okay thankyou. this has really helped me.

- jchick

Your welcome!

- jchick

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

- jchick

division makes things smaller

- anonymous

that makes it a little easier to understand,

- jchick

Ok good

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