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Math Help - dis/continuous function - Sketch Graph

  1. #1
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    dis/continuous function - Sketch Graph

    Hello,
    how can I sketch the Graph of the following function?
    ----------4 x < 2
    f(x) = {
    ----------x 2 ≤ x

    and I've to know if this function is continuous or not but I think that I can solve this after sketching the function ?


    Infi
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Infi View Post
    Hello,
    how can I sketch the Graph of the following function?
    ----------4 x < 2
    f(x) = {
    ----------x 2 ≤ x

    and I've to know if this function is continuous or not but I think that I can solve this after sketching the function ?


    Infi
    Hi Infi,

    f(x) = \left \{\begin {array}{cc}4, & \mbox{ if } x < 2 \\ x^2, & \mbox{ if } x \ge 2 \end {array}\right

    This is a piecewise function. The first branch is a horizontal line at F(x) = 4 for all x less than 2. f(2) is not defined on this branch.

    The second branch is the right branch of a parabola starting at f(x) = x^2 for all x greater than or equal to 2.

    Since the second branch includes f(2) = 4, the function is continuous for all values of x.

    dis/continuous function - Sketch Graph-screen1.jpg
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