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Math Help - diagrams and graphs

  1. #1
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    Thumbs up diagrams and graphs

    please help!!
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  2. #2
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    Quote Originally Posted by carlasader View Post
    please help!!

    Hello,

    to #2:

    The coordinates of the point must satisfy the equation of the function. That means if you plug in the coordinates the equation must be true:

    5 = (2-1)^2 \cdot (2+a)~ \Longrightarrow ~ 5 = 1 \cdot (2+a) ~ \Longrightarrow ~ a = 3

    The function becomes: y = f(x) = (x-1)^2 \cdot (x+3).

    This is a cubic function with the domain \mathbb{R}. The y-values are running from -\infty to +\infty.

    The function has a zero at x = -3 and a second zero at x = 1 where the graph touches the x-axis. Therefore:

    y < 0 for x < -3 and y > 0 for x > -3

    To draw the function g(x) = |f(x)| reflect the parts of the graph which are below the x-axis over / at(?) the x-axis:

    g(x) = \left\{ \begin{array}{c}-f(x), x < -3 \\f(x), x \geq -3\end{array} \right.

    The graph of g is sketched in red.
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