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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)

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  1. anonymous
    • one year ago
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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....

  2. anonymous
    • one year ago
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    @whpalmer4 can you please help

  3. anonymous
    • one year ago
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    @ashy98

  4. jchick
    • one year ago
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    What happens if we add or subtract something from the result of a function?

  5. anonymous
    • one year ago
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    I have no clue...

  6. jchick
    • one year ago
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    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.

  7. jchick
    • one year ago
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  8. anonymous
    • one year ago
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    so if you add or subtract something it will shift the line up and down?

  9. jchick
    • one year ago
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    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?

  10. jchick
    • one year ago
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    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.

  11. jchick
    • one year ago
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    how do we shift right or left?

  12. anonymous
    • one year ago
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    adding a positive or negative integer with in the parenthesis?

  13. jchick
    • one year ago
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    (-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

  14. anonymous
    • one year ago
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    oh okay, that makes sense..

  15. jchick
    • one year ago
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    adding or subtracting from the argument of the function is to translate the graph to the left or the right.

  16. anonymous
    • one year ago
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    0kay.. what happens when you multiply or divide from the function?

  17. jchick
    • one year ago
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    Do you have a guess?

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

  19. jchick
    • one year ago
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    you stretch or compress it

  20. anonymous
    • one year ago
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    what does that mean?

  21. jchick
    • one year ago
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    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

  22. jchick
    • one year ago
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    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).

  23. jchick
    • one year ago
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    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).

  24. jchick
    • one year ago
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    Does that help?

  25. anonymous
    • one year ago
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    so does that mean that the slope would change from say 1 to 1/ any number higher?

  26. jchick
    • one year ago
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    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.

  27. anonymous
    • one year ago
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    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?

  28. jchick
    • one year ago
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    . It affects where it reflects

  29. jchick
    • one year ago
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    Whether or not it is across the y or x axis

  30. jchick
    • one year ago
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    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.

  31. anonymous
    • one year ago
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    ahhh okay hats making a lot more sense to me.

  32. anonymous
    • one year ago
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    now how does it affect the vertex?

  33. jchick
    • one year ago
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    You can see that the vertex moved from (3,2) to (−1,2)

  34. jchick
    • one year ago
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    And 3 - (-1)

  35. anonymous
    • one year ago
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    oh yeah, so it moves the way the graph would?

  36. jchick
    • one year ago
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    Yes

  37. jchick
    • one year ago
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    So can you solve it from here?

  38. jchick
    • one year ago
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    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)

  39. anonymous
    • one year ago
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    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?

  40. jchick
    • one year ago
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    Correct

  41. anonymous
    • one year ago
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    oh okay thankyou. this has really helped me.

  42. jchick
    • one year ago
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    Your welcome!

  43. jchick
    • one year ago
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    Think of it this way with multiplication you will get a larger number than dividing

  44. jchick
    • one year ago
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    division makes things smaller

  45. anonymous
    • one year ago
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    that makes it a little easier to understand,

  46. jchick
    • one year ago
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    Ok good

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