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3.1.6 Algebra and functions (A-level only)

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Question 30

The thermal intensity H H\,H of a heating element over a distance x x\,x from its center is modeled by the function

H(x)=A−∣5x−B∣ H(x) = A - |5x - B| H(x)=A−∣5x−B∣

where A A\,A and B B\,B are positive constants, with A>BA > BA>B.

a.

Find, giving your answers in terms of A A\,A and BBB: (i) the coordinates of the maximum point of the graph of H(x)H(x)H(x), (ii) the coordinates of the point of intersection of the graph with the yyy-axis, (iii) the coordinates of the points of intersection of the graph with the xxx-axis.

[5]
b.

Sketch the graph of H(x)H(x)H(x) and, on the same axes, add the graph with equation G(x)=2∣x∣−5G(x) = 2|x| - 5G(x)=2∣x∣−5.

[2]
c.

Given that the graphs of H(x)H(x)H(x) and G(x)G(x)G(x) intersect at the points where x=−1x = -1x=−1 and x=3x = 3x=3,

find the value of A A\,A and the value of BBB.

[5]

3.1.6 Algebra and functions (A-level only) Questions

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