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)

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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)

Mathematics
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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....
@whpalmer4 can you please help

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What happens if we add or subtract something from the result of a function?
I have no clue...
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.
1 Attachment
so if you add or subtract something it will shift the line up and down?
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?
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.
how do we shift right or left?
adding a positive or negative integer with in the parenthesis?
(-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
oh okay, that makes sense..
adding or subtracting from the argument of the function is to translate the graph to the left or the right.
0kay.. what happens when you multiply or divide from the function?
Do you have a guess?
I honestly didn't know you could before I saw this equation, so I have no clue what it will do to the graph..
you stretch or compress it
what does that mean?
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
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).
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).
Does that help?
so does that mean that the slope would change from say 1 to 1/ any number higher?
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.
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?
. It affects where it reflects
Whether or not it is across the y or x axis
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.
ahhh okay hats making a lot more sense to me.
now how does it affect the vertex?
You can see that the vertex moved from (3,2) to (−1,2)
And 3 - (-1)
oh yeah, so it moves the way the graph would?
Yes
So can you solve it from here?
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)
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?
Correct
oh okay thankyou. this has really helped me.
Your welcome!
Think of it this way with multiplication you will get a larger number than dividing
division makes things smaller
that makes it a little easier to understand,
Ok good

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