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1234Linear functions

Exercises

Exercise 1

Cyclist 1 rides from A to B with a constant speed of 20 km/h. Cyclist 2 rides from B to A with a constant speed of 25 km/h. The distance between A and B is 150 km for each cyclist. a is the distance from A and t is the time in hours.

a

Draw the graphs of both rides into the same a , t -coordinate system.

b

For each cyclist, set up the corresponding formula for the relationship between a and t .

c

After how many hours do the two cyclists meet each other? Provide an explanation for your answer.

Exercise 2

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.

a

h ( t ) = 3 t - 5

b

f ( x ) = x - 4

c

g ( x ) = -0.5 x + 4

d

k ( x ) = -2 ( x + 3 )

Exercise 3

Given the function y 1 = -4 + 5 x .

a

Draw the graph of this function and show the values of the -intercept and the gradient in the graph.

b

The graph of y 1 is shifted up the y -axis by 10 units. Determine the function rule of this new graph y 2 .

c

The graph of y 1 is reflected about the y -axis. Determine the function rule for this new graph y 3 .

Exercise 4

You here see a coordinate system with four points A B C D arranged in a square. A linear function in this coordinate system goes through point ( 1 , 5 ) .

a

Explain why the corresponding formula must be y = a x + 5 - a .

b

Which values of a produce a line that does not have any points in common with the square?

Exercise 5

Given the functions f ( x ) = 4 - 0.5 x and g ( x ) = 2 x - 1 .

a

Calculate algebraically the intersects of both functions with the axes of the coordinate system.

b

Calculate algebraically the point of intersection of the graphs.

Exercise 6

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 26 km. A participant arrives in Dokkum after 7 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 200 km.

a

What was his speed on the last stretch of the tour?

b

Assume that t is the time in hours, with t = 0 being the start of the entire tour for this participant. The total distance covered is a . Which function rule a ( t ) describes the last part of his tour?

c

This participant started the tour at the same time as I did, but I arrived in Dokkum 2 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?

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