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Functions and Graphs

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Question 223

The function T T\,T is defined for x∈Rx \in \mathbb{R}x∈R by T(x)=3∣x−6∣−15T(x) = 3|x - 6| - 15T(x)=3∣x−6∣−15. The graph of y=T(x)y = T(x)y=T(x) forms a V-shape with a vertex at point PPP.

a.

State the coordinates of the vertex PPP.

[1]
b.

Evaluate the composite TT(0)TT(0)TT(0).

[2]
c.

Determine the range of values of x x\,x for which T(x)<2x−1T(x) < 2x - 1T(x)<2x−1.

[4]
d.

Solve the equation T(∣x∣)=0T(|x|) = 0T(∣x∣)=0.

[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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