5. Draw the graph of the function defined by $f(x)=-\sqrt{x^{2}-6 x+9}$ and calculate the area of the figure enclosed by the graph of the given function and the coordinate axes.[^0]
 6. Mathematical competition for students of secondary technical and vocational schools

Celje, April 20, 2002

## PROBLEMS FOR 2nd GRADE
5. Notation $f(x)=-\sqrt{(x-3)^{2}}$ ..... 1 point
Notation $f(x)=-|x-3|$ ..... 1 point
Calculated zero $(m)$, initial value $(n): m=3, n=-3$ ..... 1 point
Graph of the function $g(x)=-(x-3)$ drawn ..... 1 point
Graph of the function $f(x)=-|x-3|$ drawn ..... 1 point
Calculated area of the triangle $S=\frac{9}{2}$ ..... 1 point
Note: If the student draws $g(x)=-x+3$ and correctly calculates the area, they get 4 points.

## Second Year