(a) By copying and completing the table below, plot graphs of P1 against t and P2 against t on the same diagram. Give all answers correct to the nearest whole number.
t 01234567
P1 P2
(b) Use your graphs to fi nd the times in days at which the two populations are equal, correct to one decimal place.
4. Let f : x → 3 x and g : x →
( 1 __
3 ) . x
(a) By copying and completing the table below, draw graphs of f and g on the same diagram for –2 ≤ x ≤ 2, x ∈ R.
x –2 –1 0 1 2
(b) Write down the co-ordinates of their only point of intersection. (c) Use your graphs to solve: (i) 3 x = 4·5, correct to one decimal place, (ii) 2
( 1 __
3 ) = 13, correct to one decimal place. x 5. The functions f (x) = 4( √
__ 2 ) x and g (x) = a – (x – 2)2 are shown in the diagram. The graphs intersect at
A on the y-axis and at B, the point at which g (x) has its maximum value. f
y B g A (c, 0)
(a) Find the co-ordinates of A. Find a. (b) Find c, the x co-ordinate of the maximum value of g. (c) Find the co-ordinates of B.
