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3.2 Algebra and Functions (A-level only)

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Question 64

Given that kkk is a positive constant,

a.

on separate diagrams, sketch the graph with equation

(i) y=k−3∣x∣y = k - 3|x|y=k−3∣x∣

(ii) y=∣3x−k2∣y = \left| 3x - \frac{k}{2} \right|y=​3x−2k​​

Show on each sketch the coordinates, in terms of kkk, of each point where the graph meets or cuts the axes.

[4]
b.

Hence find, in terms of kkk, the values of xxx for which

∣3x−k2∣=k−3∣x∣ \left| 3x - \frac{k}{2} \right| = k - 3|x| ​3x−2k​​=k−3∣x∣

giving your answers in simplest form.

[4]

3.2 Algebra and Functions (A-level only) Questions

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