Rational functions

2000006704

Level: 
B
Let \(X\) and \(Y \) be intersections of the graph of the function \(f(x) = \frac{3x-5} {2+x}\) with \(x\)- and \(y\)-axis, respectively. Find these points.
\(X = \left[\frac{5}{3};0\right]\), \(Y = \left[0;-\frac{5}{2}\right]\)
\(X = \left[-\frac{5}{2};0\right]\), \(Y = \left[0;\frac{5}{3}\right]\)
\(X = \left[0;\frac{5}{3}\right]\), \(Y = \left[-\frac{5}{2};0\right]\)
\(X = \left[\frac{5}{2};0\right]\), \(Y = \left[0;-\frac{5}{3}\right]\)

2000006701

Level: 
B
A part of the graph of the function \( f(x)=-\frac2x \) is shown in the picture. Identify which of the following statements is true.
The function \( g \) defined by \( g(x)=-\left|f(x)\right| \) is an even function.
The function \( g \) defined by \( g(x)=-\left|f(x)\right| \) is bounded below.
The function $f$ is decreasing on \( (-\infty;0)\).
The function $m$ defined by \( m(x)=f(x)-3 \) is bounded.

2000003706

Level: 
A
The length of a rectangle is extended twice its original length. How must its width be changed so that the area of the rectangle remains the same?
the width is reduced to half (of its original width)
the width is increased by half (of its original width)
the width is reduced by a quarter (of its original width)
the width is increased to double (of its original width)

2000003705

Level: 
A
A car going at a speed \(60\,\mathrm{km/h}\) covers the distance from city \(A\) to city \(B\) in \(30\) minutes. If the distance has to be covered in \(20\) minutes, how many times does the driver have to increase the speed when leaving \(A\).
\(1.5\) times
\(1.\overline{3}\) times
\(1.\overline{6}\) times
\(1.2\) times

2000003704

Level: 
A
A car going at a speed \(60\,\mathrm{km/h}\) covers the distance from city \(A\) to city B in \(30\) minutes. If the distance has to be covered in \(20\) minutes, by how many \(\mathrm{km/h}\) must the driver increase the speed when leaving \(A\).
by \(30\,\mathrm{km/h}\)
by \(20\,\mathrm{km/h}\)
by \(40\,\mathrm{km/h}\)
by \(45\,\mathrm{km/h}\)