Linear Functions

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 \(U\).
\(I = \frac{2} {3}U -\frac{4}{3};U\in [2;\infty) \)
\(I = \frac{3} {2}U - 2;U\in [2;\infty) \)
\(I = \frac{3} {2}U + 2;U\in [2;\infty) \)
\(I = \frac{2} {3}U + 2;U\in [2;\infty) \)

9000007808

Level: 
B
Given a function \(f(x) = \frac{x} {3} + 1\), find the function \(g\) such that the graph of \(g\) is symmetric with the graph of \(f\) about the \(y\)-axis.
\(g\colon y = -\frac{x} {3} + 1\)
\(g\colon y = 3x + 1\)
\(g\colon y = -3x + 1\)
\(g\colon y = -\frac{x} {3} - 1\)
Such a function does not exist.