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Functions and Graphs

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Question 13

Coordinate axes and a V-shaped graph with vertex P.

The diagram shows a sketch of y=2∣x−3∣−3y = 2|x - 3| - 3y=2∣x−3∣−3

The vertex of the graph is at point PPP.

a.

Find the coordinates of point PPP.

[2]
b.

Solve the equation 3−x=2∣x−3∣−33 - x = 2|x - 3| - 33−x=2∣x−3∣−3

[2]
c.

Find the gradient of the line joining the origin to point PPP.

[1]
d.

A line l l\,l has equation y=axy = axy=ax, where a a\,a is a constant. Given that l l\,l intersects y=2∣x−3∣−3y = 2|x - 3| - 3y=2∣x−3∣−3 at least once, find the range of possible values of aaa, writing your answer in set notation.

[3]
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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