Cyclist rides from A to B with a constant speed of km/h. Cyclist rides from B to A with a constant speed of km/h. The distance between A and B is km for each cyclist. is the distance from A and is the time in hours.
Draw the graphs of both rides into the same -coordinate system.
For each cyclist, set up the corresponding formula for the relationship between and .
After how many hours do the two cyclists meet each other? Provide an explanation for your answer.
For each of the following linear functions, calculate the - and -axis intersects. Then use the -intercept and gradient to draw the corresponding graphs. Use these graphs to check the intersects you calculated earlier.
Given the function .
Draw the graph of this function and show the values of the -intercept and the gradient in the graph.
The graph of is shifted up the -axis by units. Determine the function rule of this new graph .
The graph of is reflected about the -axis. Determine the function rule for this new graph .
You here see a coordinate system with four points arranged in a square. A linear function in this coordinate system goes through point .
Explain why the corresponding formula must be .
Which values of produce a line that does not have any points in common with the square?
Given the functions and .
Calculate algebraically the intersects of both functions with the axes of the coordinate system.
Calculate algebraically the point of intersection of the graphs.
The so-called 'Elfstedentocht' is an ice-skating tour along eleven Frisian towns. The last part, from Dokkum to Leeuwarden, is an almost straight stretch of km. A participant arrives in Dokkum after hours. He manages to keep a constant speed over this last stretch. He arrives in Leeuwarden after three quarters of an hour, and in total he has completed a tour of km.
What was his speed on the last stretch of the tour?
Assume that is the time in hours, with being the start of the entire tour for this participant. The total distance covered is . Which function rule describes the last part of his tour?
This participant started the tour at the same time as I did, but I arrived in Dokkum hours later than him. Like him, I managed to skate with a constant speed over the last stretch, but it took me an hour to do so. Which formula describes my skate from Dokkum to Leeuwarden?