text: # Exam-Style Questions on Graphing Functions
  
  ## Problems on Graphing Functions adapted from questions set in previous exams.
  
  ### 1.
  
  IGCSE Extended
  
  The table shows some values (rounded to one decimal place) for the function $$y=\frac{2}{x^2}-x, x\neq 0$$.
  
   $$x$$ $$y$$ -3 -2 -1 -0.5 0.5 1 2 3 4 3.2 2.5 8.5 7.5 1 -2.8
  
  (a) Complete the table of values.
  
  (b) Draw the graph of $$y=\frac{2}{x^2}-x$$ for $$-3\le x \le -0.5$$ and $$0.5\le x\le 4$$.
  
  (c) Use your graph to solve the equation $$\frac{2}{x^2}-x-3=0$$
  
  (d) Use your graph to solve the equation $$\frac{2}{x^2}-x=1-2x$$
  
  (e) By drawing a suitable tangent, find an estimate of the gradient of the curve at the point where x = 1.
  
  (f) Using algebra, show that you can use the graph at $$y=0$$ to find $$\sqrt[3]2$$
  
  ### 2.
  
  IB Standard
  
  Let $$f (x)=a(x-b)^2+c$$. The vertex of the graph of $$f$$ is at (4, -3) and the graph passes through (3, 2).
  
  (a) Find the value of $$c$$.
  
  (b) Find the value of $$b$$.
  
  (c) Find the value of $$a$$.
  
  The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
  
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