On a single diagram, sketch the graphs of $y=\left| 2x-p \right|$ and $y=qx$ where the following

Question

On a single diagram, sketch the graphs of $y=\left| 2x-p \right|$ and $y=qx$ where the following conditions are satisfied, indicating the axial intercepts.

• $p$ and $q$ are constants, $p > 1$ and $q > 0$, and

• the graphs have only one point of intersection.[2]

State the least value of $q$.[1]
Solve the inequality $\left| 2x-p \right|>qx$, leaving your answer in terms of $p$ and $q$.[2]

Accepted Answer

Sketch intercepts $(0,p)$, $\left(\frac p2,0\right)$, and $(0,0)$, with $q\ge2$ (a) $q_{\min}=2$ (b) $x<\frac p{2+q}$

2024 TJC P1 Q2

2024 TJC P1 Q2

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