advanced funtions

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what are similarities and differences between y=x line and a power funtion with an odd degree?

i wrote that:
similarties
both have funtions pass through the orgin. both have one y int and one xint. both have the same ending. both have the same domain and range. beahvior from quadrant 3 to quadrant 1.

differnce
the shape is different.

i need more for this... please help me... THANKS ALOT!!!

  • advanced funtions -

    similarties:
    1. both pass through the origin
    2. both have the same domain and range (ℝ)
    3. both have start from quadrant 3 and finish in quadrant 1.
    4. Both do not have local maximum or minimum.

    differnce
    1. the shapes are different, y=x is a straight line, the power functions are curves.
    2. The power functions have one point of inflection, at the origin, the straight line has none.
    3. The power functions are concave downwards for x<0, and concave upwards for x>0.

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