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Standard forms (p. 2)

  1. how do you find symmetry about the y and x-axis?

    eg. Image Upload 2
    make y or x equal -y and -x.

    eg. Image Upload 4

    if the answer is identical to the original formula, it is symmetrical.
  2. how do you find symmetry about the origin?
    make both x and y negative.
  3. how can you tell if a function is 1 to 1 or many-to-1?
    do the horizontal line test
  4. how do you show that a function is not 1-to-1?

    eg. Image Upload 6
    give two x values that have the same y value.

    • vertex: (-1, 2)
    • y-int: (0, 1)

    so... f(-2) = 1, f(-1) = 0
  5. how do you show that a function is 1-to-1?

    eg. Image Upload 8
    suppose that Image Upload 10 (the y value at x).

    solve both possibilities, eg Image Upload 12

    and Image Upload 14.

    Done!
  6. what is an inverse of a function? and how do you prove that two functions are inverse of each other?
    an inverse is when (gof)(x) and (fog)(x) both equal (x).

    solve both for x. they should both equal x.
  7. how do you find the inverse of a function?
    let y=x and x=y.

    isolate y and solve for y.

    replace y with f(x).
  8. what is Image Upload 16
    an exponential growth function (with a horizontal asymptote that never touches 0)
  9. what is Image Upload 18
    an exponential decay function
Author
Anonymous
ID
199872
Card Set
Standard forms (p. 2)
Description
standard forms algebra
Updated

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