## Exam-Style Question on Modulus Graph## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 467. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.

The diagram on the right shows a sketch of part of the graph:

$$ y = f(x) \quad \text{where} \quad f(x) = 3 | 5-2x | + 4 $$

(a) State the range of \(f\).

(b) Solve the equation \(f(x) = \frac{x}{3} + 20 \).

(c) Given that the equation \(f(x) = k\), where \(k\) is a constant, has two distinct roots, state the set of possible values for k.

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