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Modulus of functions and reciprocal graphsAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

  • Definition of |x|?
  • How do you solve |f(x)|=k for k0?
  • How do you solve |f(x)|=g(x)?
  • |f(x)|<k becomes?
  • |f(x)|k becomes?
  • How do you compare two moduli?
  • How do you sketch y=|f(x)|?
  • Where are the vertical asymptotes of y=\frac1{f(x)}?
  • Horizontal asymptote of y=\frac1{f(x)} when f\to\infty?
  • What does a minimum of f become on y=\frac1{f}?
  • Which points are unchanged on y=\frac1{f(x)}?
  • Can \frac1{f(x)} ever equal 0?
  • Why check answers to |f|=g?

Exam questions on Modulus of functions and reciprocal graphs

  1. Let f(x)=∣2x−1∣\mathrm{f}(x)=|2x-1|.
    Solve f(x)=x+4\mathrm{f}(x)=x+4.2 marks
  2. Let f(x)=x2+2x−3\mathrm{f}(x)=x^2+2x-3 and g(x)=1f(x)\mathrm{g}(x)=\dfrac{1}{\mathrm{f}(x)}.
    Find the coordinates of the turning point of y=g(x)y=\mathrm{g}(x) and state its nature.2 marks
  3. Let f(x)=x2−4x\mathrm{f}(x)=x^2-4x.
    Solve ∣f(x)∣=4|\mathrm{f}(x)|=4.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).