EduNinja

IB Maths AI SL 2.3 Graphing functions

IB Maths AI SL 2.3 Graphing functions
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise sketching graphs of functions—including transformations, rational, exponential and trigonometric—using key features like intercepts, asymptotes, turning points…

How this is tested

  • sketch y = P(t) as smooth, increasing, concave-down from (5, 0), passing near (10, 150)
  • sketch y = f(2x − 2) by horizontally compressing f(x) by factor ½ and shifting right by 1 unit
  • sketch v(t) or x(t) with correct shape over specified interval 0 ≤ t ≤ 6

Question 10(c)

[Maximum number: 2]

At 12:05 pm, Navam starts draining water from a small reservoir into an empty pond.
He controls the rate the water is drained so that the volume of water remaining in the reservoir, V m3V \mathrm{~m}^{3}, varies inversely with the time, t, where t is the number of minutes after 12:00 pm.
At 12:05 pm, the volume of water in the reservoir is 300 m3300 \mathrm{~m}^{3}.

On the same diagram, sketch the graph of y=P(t), where P is the volume of water in the pond.