Linear functions

1103171403

Level:

Determine whether the line drawn in the picture is the graph of a linear function of the variable \(x\). If so, find the formula for the function.

It is not the graph of a linear function in the picture.

\( y=5 \)

\( x=5 \)

\( y=5x \)

1103171402

Level:

There are graphs of three linear functions in the picture. Choose the formula which corresponds to all three functions.

\( y=dx-2;\ d\in\mathbb{R}^- \)

\( y=dx-2;\ d\in\mathbb{R}^+ \)

\( y=2x+d;\ d\in\mathbb{R}^- \)

\( y=-2x+d;\ d\in\mathbb{R}^+ \)

1103171401

Level:

There are graphs of three linear functions in the picture. Choose the formula which corresponds to all three functions.

\( y=m;\ m\in\mathbb{R}^- \)

\( y=m;\ m\in\mathbb{R}^+ \)

\( y=mx;\ m\in\mathbb{R}\setminus\{0\} \)

\( y=x+m;\ m\in\mathbb{R}^- \)

The picture shows velocity-time graphs of movements of cars \( A \), \( B \), \( C \) and \( D \). Which of the cars speeds up with constant acceleration of \( 0.8\,\frac{\mathrm{m}}{\mathrm{s}^2} \)? \[ \] Hint: An acceleration \( a \) is the rate of change of velocity \( \Delta v \) of an object with respect to time \( \Delta t \), i.e. \( a=\frac{\Delta v}{\Delta t} \).

\( A \)

\( B \)

\( C \)

\( D \)

1103171503

Level:

Trains run between the towns \( M \) and \( N \) in both directions. The lines in the distance-time diagram correspond to the uniform movements of trains \( A \), \( B \), \( C \) and \( D \) between the towns. Find out which of the trains is the fastest. \[ \] Note: The distance-time diagram as seen in the picture is a graphical representation of trains operating schedule for a certain rout (or routs). Connections are displayed as broken-lines or line segments in rectangular coordinate system, where horizontal is the time axis with the time during an operating day and vertical is the distance axis with distances of the traffic nodes (e.g. railroad stations, cities) from one chosen reference node (in our case the town \( N \)). Connections in one direction (from \( N \) to \( M \)) are displayed by the lines skewed to the right (trains \( B \) and \( C \)) and back-connections in other direction (from \( M \) to \( N \)) are displayed by the lines skewed to the left (trains \( A \) and \( D \)).

\( A \)

\( B \)

\( C \)

\( D \)

1103171502

Level:

Current-Voltage characteristic of a conductor is a relationship, usually represented as a graph, between the current \( I \) through the conductor and the voltage \( U \) across the conductor. The picture shows two characteristics: of a metal conductor (red colour) and of an electrolytic conductor (black colour). At what voltages need to be conductors connected so that the current is the same in both of them?

\( 10\,\mathrm{V} \)

\( 16\,\mathrm{V} \)

\( 8\,\mathrm{V} \)

\( 9.5\,\mathrm{V} \)

1103171501

Level:

Ohm's law states that the current \( I \) through a conductor is directly proportional to the voltage \( U \) between the endpoints of the conductor. This relationship is described by the equation \( I=\frac UR \), where \( R \) is the resistance of the conductor. Current-voltage characteristics of the conductors \( A \) and \( B \) are in the picture. Which of the conductors has greater resistance?