Rational functions

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 \(45\,\mathrm{km/h}\)

2000003701

Level: 
A
Group of mountaineers would climb the top of the mountain at an ascent speed of \(400\,\mathrm{m}\) per day in \(10\) days. However, due to the weather, they have to conquer the peak in \(8\) days. How many more meters per day do they have to cover?
\(100\) meters more
\(80\) meters more
\(120\) meters more
\(90\) meters more

1103129201

Level: 
B
The thin lens equation \( \frac1a+\frac1{a'}=\frac1f \) describes the quantitative relationship between the object distance \( a \), the image distance \( a' \), and the focal length \( f \). Let the focal length of a thin lens be \( 0{.}5\,\mathrm{m} \). Choose the picture that shows the object distance vs. image distance graph, if \( a\in [0.1\,\mathrm{m};0.4\,\mathrm{m}]\cup [0.6\,\mathrm{m};3.0\,\mathrm{m}] \).

1103108604

Level: 
A
The hall’s floor needs a new tiling. All tiles used will be of the same size. The picture shows the graph of the function describing dependence of the number \( p \) of tiles needed in the hall on the area \( S \) of one tile. What is the area of the hall’s floor?
\( 10.5\,\mathrm{m}^2 \)
\( 1\:050\,\mathrm{m}^2 \)
\( 2\:100\,\mathrm{m}^2 \)
\( 42\,\mathrm{m}^2 \)