Graphical Transformations: Eduqas GCSE Higher June 2019 Paper 2 Q17

Higher June 2019 Paper 2 Q17

EduqasHigherCurrent spec7 marksGraphical Transformations Transformations of Shapes

17.

(a) The diagram shows a sketch of \(y = f(x)\).

On the same diagram, sketch the curve \(y = -f(x)\).
Mark clearly the coordinates of any point where this curve crosses an axis. [2]

Sketch of y = f(x): a straight line rising from the lower left to the point (0, −2) on the y-axis, then a curve rising to a maximum below the x-axis and falling again; the curve does not cross the x-axis

(b) The diagram shows a sketch of \(y = g(x + 2)\).

On the same diagram, sketch the curve \(y = g(x - 1)\).
Mark clearly the coordinates of the points where this curve crosses the \(x\)-axis. [3]

Sketch of y = g(x + 2): a curve with a maximum to the left, crossing the x-axis at −2, a minimum between −2 and 0, then crossing at the origin and rising steeply

(c) Enlarge the triangle, shown on the grid below, by a scale factor of \(-\frac{1}{2}\) with \((2, 1)\) as the centre of the enlargement. [2]

Grid with x and y from −10 to 10 showing a right-angled triangle with vertices (−8, 3), (−8, 7) and (−2, 3)

Scheme	Marks	Comments
Reflection in the \(x\)-axis	M1
\((0, 2)\)	A1	Accept 2 indicated correctly on the \(y\)-axis

Mark scheme (b)

Scheme	Marks	Comments
Horizontal translation	B1	Any horizontal translation without including any other transformation
Correct translation with \((1, 0)\) and \((3, 0)\) indicated on the \(x\)-axis	B2	Accept indication of 1 and 3 on the \(x\)-axis with the correct translation B1 for a correct translation with only one of the values 1 and 3 indicated, or for a horizontal translation with \((-1, 0)\) and \((1, 0)\) indicated on the \(x\)-axis as intersections, or for a horizontal translation to show \(y = g(x)\) with \((0, 0)\) and \((2, 0)\) indicated on the \(x\)-axis as intersections