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Functions and Graphs

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Question 135

Sketch of a V-shaped graph with coordinate axes

The graph shows a sketch of y=∣mx+n∣y = |mx+n|y=∣mx+n∣, where m>0 m>0\,m>0 and n<0n<0n<0.

a.

The points of intersection with the axes are (0,2)(0, 2)(0,2) and (2/3,0)(2/3, 0)(2/3,0). Determine the equation of the graph in the form y=∣mx+n∣y = |mx+n|y=∣mx+n∣.

[2]
b.

Given that the graphs of y=∣3x−2∣y = |3x - 2|y=∣3x−2∣ and y=ax+1y = ax + 1y=ax+1 have two distinct points of intersection, and that −3/2<a<3-3/2 < a < 3−3/2<a<3, determine the x x\,x coordinates of the points of intersection of these graphs, giving your answers in terms of aaa.

[7]
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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