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Math Help - find values for m and n so function is continuous

  1. #1
    Member sluggerbroth's Avatar
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    find values for m and n so function is continuous

    f(x)= mx, x<3
    n, x=3
    -2x+9 x>3
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    Re: find values for m and n so function is continuous

    First pick a value for x>3 i.e. x=4 then solve n such that -2(4)+9 = n

    Once you know what n is then for x=3, solve mx=n, will give you m.
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    Re: find values for m and n so function is continuous

    Quote Originally Posted by sluggerbroth View Post
    f(x)= mx, x<3
    n, x=3
    -2x+9 x>3
    You want to find m~\&~n so that {\lim _{x \to {3^ + }}}f(x) = {\lim _{x \to {3^ - }}}f(x).
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  4. #4
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    Re: find values for m and n so function is continuous

    Hello, sluggerbroth!

    \text{Find values for }m\text{ and }n\text{ so that }f(x)\text{ is continuous.}

    . . f(x) \;=\;\begin{Bmatrix}mx & \text{ if } x < 3 \\ n & \text{ if }x = 3 \\ -2x+9 & \text{ if }x > 3 \end{array}

    Make a sketch.

    When x < 3, we have a line through the origin with slope m.

    When x = 3, we have a point (3,n).

    When x > 3, we have the line y \:=\:-2x + 9
    . . It has y-intercept 9 and slope -2.

    We want the three graphs to "meet" at x = 3.

    Code:
         \|
          *
          |\
          | \
          |  \
          |   \
          |    \
          |     \     *
          |      \  *
          |       o
          |     * :\
          |   *   : \
          | *     :  \
      - - * - - - + - * - -
        * |       3    \
          |
    Can you work it out?

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