C

2010012201

Level: 
C
Function \( f \) is given completely by the graph. Identify which of the following statements is true.
\( f(x)=-\left|x^2-4\right|;\ x\in[ -3;3] \)
\( f(x)=-\left|x^2+4\right|;\ x\in[ -3;3]\)
\( f(x)=-\left|x^2\right|-4;\ x\in[ -3;3]\)
\( f(x)=\left|-x^2\right|-4;\ x\in[ -3;3] \)

2010011206

Level: 
C
Consider the system \[\begin{aligned} y & = \frac{k} {x}, & & \\y & = a, & & \end{aligned}\] where \(a\), \(k\) are real parameters and \(x\), \(y\) are real variables. Determine the conditions for \(a\) and \(k\) so that the system has a unique solution in \(\mathbb{R}^{+}\times \mathbb{R}^{-}\).
\(a < 0\) and \(k < 0\)
\(a < 0\) and \(k > 0\)
\(a > 0\) and \(k < 0\)
\(a > 0\) and \(k > 0\)

2010011202

Level: 
C
Students registered for sports camps. For the biking camp registered by \( 12 \) students more than for the boating camp. After some time one of the students switched his registration from the boating camp to the biking camp. Now, there is three times more bikers than boaters. How many students registered originally for the biking camp?
\( 20 \)
\( 21 \)
\( 7 \)
\( 8 \)

2010011201

Level: 
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which inequality is it?
\( y \geq -\frac32x+\frac{7}2 \)
\( y \leq -\frac32x+\frac{7}2 \)
\( y > -\frac32x+\frac{7}2 \)
\( y < -\frac32x+\frac{7}2 \)