Higher November 2020 Paper 1 Q25
25 The curve with equation \(y = \mathrm{g}(x)\) is transformed to the curve with equation \(y = -\mathrm{g}(x)\) by the single transformation T.
The diagram shows the graph of \(y = \mathrm{f}(x)\)
| Scheme | Marks |
|---|---|
| Reflection in \(y = 0\) | B1 |
| (1) |
Notes
B1: accept alternative for \(y = 0\) e.g. \(x\) axis ; if more than one transformation then B0
| Scheme | Marks |
|---|---|
| U shaped curve through (2, 6) (3, 0) (5, −6) (7, 0) (8, 6) | B2 |
| (2) | |
| (3 marks) |
Notes
B2: for a U shaped curve passing through (2, 6) (3, 0) (5, −6) (7, 0) (8, 6)
If not B2 then award B1 for either
\(2\mathrm{f}(x - 1)\) passing through at least 3 points from (2, 6) (3, 0) (5, −6) (7, 0) (8, 6)
or
\(2\mathrm{f}(x + 1)\) passing through (0, 6) (1, 0) (3, −6) (5, 0) (6, 6)
or
\(2\mathrm{f}(x)\) passing through all of (1, 6) (2, 0) (4, −6) (6, 0) (7, 6)
or
\(\mathrm{f}(x - 1)\) passing through all of (2, 3) (3, 0) (5, −3) (7, 0) (8, 3)
or
\(2\mathrm{f}(x \pm k)\) passing through all of \((1 \pm k, 6)\) \((2 \pm k, 0)\) \((4 \pm k, -6)\) \((6 \pm k, 0)\) \((7 \pm k, 6)\)
or
A clear translation of the curve using the vector \(\begin{pmatrix} 1 \\ k \end{pmatrix}\)