Discia GCSE Maths › Algebra › Transforming Graphs y=f(x)

Transforming Graphs y=f(x) worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 36 marks Sheet 1
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  1. 4 marks

    The diagram shows part of the graph of \(y = f(x)\).

    The point \(P\), marked on the curve, has coordinates \((3, 1)\).

    A parabola drawn on a coordinate grid with one point marked on it-21234-5-4-3-2-112345670xyP
    (a)

    Write down the coordinates of the image of \(P\) on the graph of \(y = f(x) + 3\).

    (b)

    Write down the coordinates of the image of \(P\) on the graph of \(y = f(x + 3)\).

  2. 4 marks

    Here is part of the graph of \(y = f(x)\).

    The point \(P\), marked on the curve, has coordinates \((5, 7)\).

    A parabola drawn on a coordinate grid with one point marked on it12345-4-3-2-1123456780xyP
    (a)

    Write down the coordinates of the image of \(P\) on the graph of \(y = -f(x)\).

    (b)

    Write down the coordinates of the image of \(P\) on the graph of \(y = f(-x)\).

  3. 3 marks

    Here is part of the graph of \(y = f(x)\).

    Its turning point \(T\) is at \((-1, -1)\).

    A parabola drawn on a coordinate grid with its turning point marked-4-3-212-3-2-11234567890xyT
    (a)

    Write down the coordinates of the turning point of the graph of \(y = f(x) - 4\).

    (b)

    Write down the coordinates of the turning point of the graph of \(y = f(x - 3)\).

    (c)

    Write down the coordinates of the turning point of the graph of \(y = -f(x)\).

  4. 3 marks

    The solid curve is the graph of \(y = f(x)\). Its turning point is at \((0, -3)\).

    The dashed curve is the image of the solid curve after a single transformation.

    Two parabolas of the same shape drawn on one coordinate grid, one solid and one dashed above or below it-4-3-21234-5-4-3-2-112345670xy
    (a)

    Describe fully the single transformation that maps the solid curve onto the dashed curve.

    (b)

    State the equation of the dashed curve in terms of \(f(x)\).

  5. 3 marks

    The solid curve is the graph of \(y = f(x)\). Its turning point is at \((2, -3)\).

    The dashed curve is the image of the solid curve after a single transformation.

    Two parabolas of the same shape drawn side by side on one coordinate grid, one solid and one dashed-4-3-2123456-5-4-3-2-112345670xy
    (a)

    Describe fully the single transformation that maps the solid curve onto the dashed curve.

    (b)

    Write down the equation of the dashed curve in terms of \(f(x)\).

  6. 4 marks

    The solid curve is the graph of \(y = f(x)\). Its turning point is at \((-1, -3)\).

    The dashed curve is the image of the solid curve after a single transformation.

    Two parabolas on one coordinate grid, one solid opening upwards and one dashed opening downwards-4-3-212-7-6-5-4-3-212345670xy
    (a)

    Describe fully the single transformation that maps the solid curve onto the dashed curve.

    (b)

    Write down the equation of the dashed curve in terms of \(f(x)\).

    (c)

    Write down the coordinates of the turning point of the dashed curve.

  7. 4 marks

    The solid curve is the graph of \(y = f(x)\), where \(f\) is an exponential function.

    The dashed curve is the image of the solid curve after a single transformation.

    Two exponential curves drawn on one coordinate grid, one solid and one dashed-4-3-2-112342468101214160xy
    (a)

    Describe fully the single transformation that maps the solid curve onto the dashed curve.

    (b)

    State the equation of the dashed curve in terms of \(f(x)\).

    (c)

    State the coordinates of the point where the dashed curve crosses the \(y\)-axis.

  8. 4 marks

    The diagram shows part of the graph of \(y = f(x)\).

    The point \(P\), marked on the curve, has coordinates \((5, 6)\).

    A parabola drawn on a coordinate grid with one point marked on it12345-5-4-3-2-112345670xyP
    (a)

    Write down the coordinates of the image of \(P\) on the graph of \(y = f(x) + 4\).

    (b)

    Write down the coordinates of the image of \(P\) on the graph of \(y = f(x + 4)\).

  9. 4 marks

    The diagram shows part of the graph of \(y = f(x)\).

    The point \(P\), marked on the curve, has coordinates \((4, 8)\).

    A parabola drawn on a coordinate grid with one point marked on it-21234-3-2-11234567890xyP
    (a)

    Write down the coordinates of the image of \(P\) on the graph of \(y = -f(x)\).

    (b)

    Write down the coordinates of the image of \(P\) on the graph of \(y = f(-x)\).

  10. 3 marks

    Here is part of the graph of \(y = f(x)\).

    Its turning point \(T\) is at \((1, -4)\).

    A parabola drawn on a coordinate grid with its turning point marked-21234-6-5-4-3-2-11234560xyT
    (a)

    Write down the coordinates of the turning point of the graph of \(y = f(x) - 2\).

    (b)

    Write down the coordinates of the turning point of the graph of \(y = f(x + 2)\).

    (c)

    Write down the coordinates of the turning point of the graph of \(y = -f(x)\).

Answers

  1. (a) \((3, 4)\)
    (b) \((0, 1)\)
  2. (a) \((5, -7)\)
    (b) \((-5, 7)\)
  3. (a) \((-1, -5)\)
    (b) \((2, -1)\)
    (c) \((-1, 1)\)
  4. (a) Translation by the vector \(\begin{pmatrix} 0 \\ 3 \end{pmatrix}\)
    (b) \(y = f(x) + 3\)
  5. (a) Translation by the vector \(\begin{pmatrix} -2 \\ 0 \end{pmatrix}\)
    (b) \(y = f(x + 2)\)
  6. (a) Reflection in the \(x\)-axis
    (b) \(y = -f(x)\)
    (c) \((-1, 3)\)
  7. (a) Reflection in the \(y\)-axis
    (b) \(y = f(-x)\)
    (c) \((0, 1)\)
  8. (a) \((5, 10)\)
    (b) \((1, 6)\)
  9. (a) \((4, -8)\)
    (b) \((-4, 8)\)
  10. (a) \((1, -6)\)
    (b) \((-1, -4)\)
    (c) \((1, 4)\)

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