2023 CJC C1BT Q5 [Modified]
2023 CJC C1BT Q5 [Modified]
13 marks
Block Test
- Describe a sequence of three transformations which transforms the graph of \(y=x-\frac{1}{2x+4}\) to the graph of \(y=-2\left( x+2 \right)+\frac{1}{x}\).[3]
- The diagram shows the graph of \(y=\mathrm{f}\left( x \right)\). The curve passes through the points \(\left( -3,-2 \right)\), \(\left( -1,0 \right)\), \(\left( 0,1 \right)\), \(\left( 1,2 \right)\) and \(\left( 3,0 \right)\), and has a horizontal asymptote at \(y=-\frac{1}{2}\).On separate diagrams that are clearly labelled, sketch the graphs of
- \(y=\frac{1}{\mathrm{f}\left( x \right)}\),[4]
- \(y=\mathrm{f}\left( \left| x \right|-1 \right)\),[3]
- \(y=\mathrm{f}\left( 2x+1 \right)\).[3]
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Answer:(a) Reflect in the \(y\)-axis, translate \(2\) units in the negative \(x\)-direction, then stretch by scale factor \(2\) parallel to the \(y\)-axis (b)(i) Vertical asymptotes \(x=-1\) and \(x=3\); left- and right-hand horizontal asymptotes \(y=-2\) and \(y=0\), respectively; key points \(\left(-3,-\frac12\right)\), \((0,1)\), and \(\left(1,\frac12\right)\) (b)(ii) Symmetric about the \(y\)-axis, through \((0,0)\), \((\pm1,1)\), \((\pm2,2)\), and \((\pm4,0)\), with maxima \((\pm2,2)\) (b)(iii) Through \((-2,-2)\), \((-1,0)\), \(\left(-\frac12,1\right)\), \((0,2)\), and \((1,0)\), with left-hand horizontal asymptote \(y=-\frac12\)
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