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1.2.12 The modulus function (A-level only)

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Question 1

The height of a laser beam trajectory relative to a datum is modeled by the function H(x)H(x)H(x), where

H(x)=2∣3x−9∣+4,x≥0 H(x) = 2|3x - 9| + 4, \quad x \ge 0 H(x)=2∣3x−9∣+4,x≥0

The minimum point on the beam's path is at the vertex VVV.

a.

Determine the coordinates of VVV.

[2]
b.

Find the values of x x\,x for which H(x)=x+7H(x) = x + 7H(x)=x+7.

[4]
c.

Consider the family of linear paths defined by G(x)=kx+1G(x) = kx + 1G(x)=kx+1, where k k\,k is a constant. Given that the equation H(x)=G(x)H(x) = G(x)H(x)=G(x) has exactly two distinct solutions,

find the range of possible values for kkk.

[4]

1.2.12 The modulus function (A-level only) Questions

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