The graph of \(y = \mathrm{f}(x)\) intersects the \(x\)-axis at the point \((a, 0)\) and the \(y\)-axis at the point \((0, b)\). The graph of \(y = \mathrm{f}(x)\) is shown in Fig. \(1\). The scales on the \(x\)- and \(y\)-axes are the same. Sketch the graph of \(y = \mathrm{f}^{-1}(x)\) on Fig. \(1\), labelling the intersections with the axes. [1] Fig. 1 The graph of \(y = \mathrm{f}(x)\) is also shown in Fig. \(2\). The scales on the \(x\)- and \(y\)-axes are the same. Sketch the graph of \(y = 2\mathrm{f}^{-1}(x - 1)\) on Fig. \(2\), labelling the intersection with the \(x\)-axis. [2] Fig. 2 The graph of \(y=g(x)\) intersects the \(x\)-axis at the points \((s,0)\), \((t,0)\) and \((u,0)\) and the \(y\)-axis at the point \((0,v)\). The graph of \(y=g(x)\) is shown in Fig. 3.1. Sketch the graph of \(y=|g(x)|\) on Fig. 3.2, labelling the points where the graph intersects or touches the axes. [2] Fig. 3.1 Fig. 3.2 The graph of \(y=g(x)\) is also shown in Fig. 4.1. Sketch the graph of \(y=g(|x|)\) on Fig. 4.2, labelling the points where the graph intersects or touches the axes. [2] Fig. 4.1 Fig. 4.2 The curve \(C\) has parametric equations \(x=t^2,\qquad y=2t+3,\qquad \text{for}\hspace{0.5em}-4\leqslant t\leqslant 4.\) Sketch the graph of \(C\).[1] Mark on your sketch the coordinates of the points where the curve \(C\) meets the axes.[1] State the equations of any lines of symmetry.[1]

N2024 P2 Q5

3 marks

Free

The graph of \(y = \mathrm{f}(x)\) intersects the \(x\)-axis at the point \((a, 0)\) and the \(y\)-axis at the point \((0, b)\).
1. The graph of \(y = \mathrm{f}(x)\) is shown in Fig. \(1\). The scales on the \(x\)- and \(y\)-axes are the same.
  Sketch the graph of \(y = \mathrm{f}^{-1}(x)\) on Fig. \(1\), labelling the intersections with the axes.
  [1]
  Fig. 1
2. The graph of \(y = \mathrm{f}(x)\) is also shown in Fig. \(2\). The scales on the \(x\)- and \(y\)-axes are the same.
  Sketch the graph of \(y = 2\mathrm{f}^{-1}(x - 1)\) on Fig. \(2\), labelling the intersection with the \(x\)-axis.
  [2]
Fig. 2
The graph of \(y=g(x)\) intersects the \(x\)-axis at the points \((s,0)\), \((t,0)\) and \((u,0)\) and the \(y\)-axis at the point \((0,v)\).
1. The graph of \(y=g(x)\) is shown in Fig. 3.1.
  Sketch the graph of \(y=|g(x)|\) on Fig. 3.2, labelling the points where the graph intersects or touches the axes.
  [2]
Fig. 3.1
Fig. 3.2
1. The graph of \(y=g(x)\) is also shown in Fig. 4.1.
  Sketch the graph of \(y=g(|x|)\) on Fig. 4.2, labelling the points where the graph intersects or touches the axes.
  [2]
Fig. 4.1
Fig. 4.2
The curve \(C\) has parametric equations
\(x=t^2,\qquad y=2t+3,\qquad \text{for}\hspace{0.5em}-4\leqslant t\leqslant 4.\)
1. Sketch the graph of \(C\).[1]
1. Mark on your sketch the coordinates of the points where the curve \(C\) meets the axes.[1]
2. State the equations of any lines of symmetry.[1]

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