standard_description: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
problem_activity: Task
Sketch  graphs of the functions $f$ and $F$ given by $f(x)= |x|$ and $F(x) = x^2$
for $-2 \leq x \leq 2$.
Suppose $g$ is the function given by  $g(x) = \frac{f(x)}{x}$ for  $x \neq 0$ and
$G$ is the function given by  $G(x) = \frac{F(x)}{x}$ for $x \neq 0$.
Sketch  graphs of the functions $g$ and $G$  for $x \neq 0$ and $-2 \leq x \leq 2$.
Is there a natural way to define $g$ and $G$ when $x =0$? Explain.


aligns: no