7. Find the point of intersection for the following pairs of functions by graphing each function.


(i) f (x) = − x + 3 and g(x) = 2x − 6


(ii) f (x) = − x + 3 and h(x) = x + 1 (iii) g(x) = − 2x + 10 and h(x) = 4 − x (iv) h(x) = x + 4 and g(x) = 2x + 7


8. Find the point of intersection for the following pairs of functions by graphing each function.


(i) h(x) = 2x − 7 and g(x) = x − 4 (ii) f (x) = − 5x + 3 and g(x) = 5x − 7 (iii) g(x) = − x − 2 and h(x) = x + 4 (iv) h(x) = − 2x − 3 and f (x) = x + 3


9. (a)


Find the point of intersection for the following pairs of functions by graphing each function fi rst.


(i) y = x + 5 and y = 2x + 7 (ii) y = − 2x + 4 and y = 2x − 8 (iii) y = − 2x − 2 and y = 2x + 6 (iv) y = − 2x + 8 and y = x − 1


(b) Using algebra, fi nd the point of intersection of the two functions in each of the pairs of functions in part (a).


10. The function h(t) = 2t + 4 describes the height h of a rocket off the ground at time t , where height is measured in metres and time is measured in seconds.


(i) What is the height of the rocket from the ground at t = 0 ?


(ii) What is the height of the rocket after 5 seconds?


(iii) Graph the function on the coordinate plane.


(iv) Find the height of the rocket after 100 seconds.


(v) How many seconds does it take for the rocket to reach a height of 596 metres?


(vi) How many seconds does it take for the rocket to reach a height of 1 004 metres?


Taking it FURTHER


11. Sandra is mowing lawns for a summer job. For every mowing job, she charges an initial fee of €10 plus a constant fee for each hour of work. Her fee for a 5-hour job, for example, is €35. Let f (t) stand for Sandra’s fee for a single job f (measured in euros) as a function of the number of hours t it took her to complete it.


(i) What fee does Sandra charge per hour?


(ii) Write the function’s f (t) formula. (iii) Graph the function. (iv) Using your graph, fi nd how many hours Sandra would have to work for on one job to earn €42.


12. A phone company is off ering its customers the following two 12-month phone plans. ●


●


Plan A: You can buy a new phone for €60 and pay a monthly fl at rate of €40 per month for unlimited calls.


Plan B: You get a new phone for free and pay a monthly fl at rate of €50 per month for unlimited calls.


(i) Write a function to represent the amount charged on plan A.


(ii) Write a function to represent the amount charged on plan B.


(iii) Graph both functions on the same coordinate plane to show the cost up to 12 months.


(vi) Using your graph, fi nd when the cost will be equal with both plans.


(v)


If you were going to use the phone for four months, which plan would be the best value?


(vi) If you were going to use the phone for two years, which phone would be the best value?


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Linking Thinking 1


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