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Functions and Graphs

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Question 202

The temperature TTT (in ∘C^{\circ}\text{C}∘C) of a chemical reaction at time t t\,t minutes is modeled by a continuous piecewise linear function T=f(t)T = f(t)T=f(t). The graph of T=f(t)T = f(t)T=f(t) is described as follows:

  • For t≤−2t \le -2t≤−2, the temperature is constant at T=−3T = -3T=−3.
  • For −2≤t≤4-2 \le t \le 4−2≤t≤4, the temperature increases linearly from (−2,−3)(-2, -3)(−2,−3) through (0,1)(0, 1)(0,1) to (4,9)(4, 9)(4,9).
  • For t≥4t \ge 4t≥4, the temperature remains constant at T=9T = 9T=9.
a.

Sketch the graph of y=f(−t)y = f(-t)y=f(−t).

[2]
b.

Sketch the graph of y=2f(t)−5y = 2f(t) - 5y=2f(t)−5.

[2]
c.

Sketch the graph of the derivative y=f′(t)y = f'(t)y=f′(t).

[2]
Markscheme

Functions and Graphs Questions

  1. A Level
  2. /Maths
  3. /Functions and Graphs

471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.

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