Math Help - diagrams and graphs

1. diagrams and graphs

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.