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anonymous
 one year ago
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
 one year ago
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 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
 one year ago
Best ResponseYou've already chosen the best response.0@whpalmer4 can you please help

jchick
 one year ago
Best ResponseYou've already chosen the best response.2What happens if we add or subtract something from the result of a function?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2If 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so if you add or subtract something it will shift the line up and down?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2Now 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
 one year ago
Best ResponseYou've already chosen the best response.2Yes, 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
 one year ago
Best ResponseYou've already chosen the best response.2how do we shift right or left?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0adding a positive or negative integer with in the parenthesis?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2(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
 one year ago
Best ResponseYou've already chosen the best response.0oh okay, that makes sense..

jchick
 one year ago
Best ResponseYou've already chosen the best response.2adding or subtracting from the argument of the function is to translate the graph to the left or the right.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00kay.. what happens when you multiply or divide from the function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I honestly didn't know you could before I saw this equation, so I have no clue what it will do to the graph..

jchick
 one year ago
Best ResponseYou've already chosen the best response.2you stretch or compress it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what does that mean?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2if 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
 one year ago
Best ResponseYou've already chosen the best response.2Horizontal Changes A horizontal stretching is the stretching of the graph away from the yaxis. A horizontal compression is the squeezing of the graph towards the yaxis. 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
 one year ago
Best ResponseYou've already chosen the best response.2Vertical Changes A vertical stretching is the stretching of the graph away from the xaxis. A vertical compression is the squeezing of the graph towards the xaxis. 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).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so does that mean that the slope would change from say 1 to 1/ any number higher?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2if 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 yaxis.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh 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
 one year ago
Best ResponseYou've already chosen the best response.2. It affects where it reflects

jchick
 one year ago
Best ResponseYou've already chosen the best response.2Whether or not it is across the y or x axis

jchick
 one year ago
Best ResponseYou've already chosen the best response.2for 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 xaxis.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahhh okay hats making a lot more sense to me.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now how does it affect the vertex?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2You can see that the vertex moved from (3,2) to (−1,2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah, so it moves the way the graph would?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2So can you solve it from here?

jchick
 one year ago
Best ResponseYou've already chosen the best response.2f(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
 one year ago
Best ResponseYou've already chosen the best response.0so 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay thankyou. this has really helped me.

jchick
 one year ago
Best ResponseYou've already chosen the best response.2Think of it this way with multiplication you will get a larger number than dividing

jchick
 one year ago
Best ResponseYou've already chosen the best response.2division makes things smaller

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that makes it a little easier to understand,
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