C

9000007207

Level: 
C
Identify a function which has the following three properties: it has at least one minimum or maximum, it is an increasing function and the range of this function is the set of all nonnegative numbers.
\(f(x) = 2x - 2\), \(x\in [ 1;+\infty )\)
\(f(x) = 2x + 2\), \(x\in (-1;+\infty )\)
\(f(x) = -2x + 2\), \(x\in (-\infty ;1] \)
\(f(x) = -2x - 2\), \(x\in \mathbb{R}\)

9000007208

Level: 
C
Paul's home is \(6\, \mathrm{km}\) from the school. At the time \(t = 0\) Paul starts to walk from his home to the school along a straight street at a constant velocity \(5\, \mathrm{km}/\mathrm{h}\). Find the function which describes Paul's remaining distance to the school as a function of time.
\(s = 6 - 5t\)
\(s = 5t - 6\)
\(s = 5t\)
\(s = 5t + 6\)

9000007209

Level: 
C
A current-voltage characteristics is shown in the graph. Find the current \(I\) as a function of the voltage \(U\).
\(I = \frac{2} {3}U -\frac{4}{3};U\in [2;\infty) \)
\(I = \frac{3} {2}U - 2;U\in [2;\infty) \)
\(I = \frac{3} {2}U + 2;U\in [2;\infty) \)
\(I = \frac{2} {3}U + 2;U\in [2;\infty) \)

9000007102

Level: 
C
Consider a family \(M\) of quadratic functions, as shown in the picture. Any quadratic function in this family is given by the analytic expression \[ y = ax^{2} + bx + c \] where \(a\), \(b\) and \(c\) are real constants and \(a\not = 0\). For each function the set \(K\) denotes the set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family \(M\) differ only in ....”
the coefficient \(c\)
the coefficient \(a\)
the coefficient \(b\)
the solution set \(K\)

9000007101

Level: 
C
Consider a family \(M\) of quadratic functions, as shown in the picture. Any quadratic function in this family is given by the analytic expression \[ y = ax^{2} + bx + c \] where \(a\), \(b\) and \(c\) are real constants and \(a\not = 0\). For each function the set \(K\) denotes the set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family \(M\) differ only in ....”
the coefficient \(a\)
the coefficient \(b\)
the coefficient \(c\)
the set \(K\)

9000004905

Level: 
C
In the following list identify a statement which is not true for the function \(f\colon y = |\log (x - 3) - 1|\).
The function \(f\) is increasing on the domain.
The domain of the function \(f\) is \((3;\infty )\).
All values of the function \(f\) are nonnegative.
The function \(f\) does not have a \(y\)-intercept.
The \(x\)-intercept of the function \(f\) is \(x = 13\).
The function \(f\) is not one-to-one.