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    Eda2f1axw Level1

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    Yi-Sin Lin - OXF.Student

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    © All Rights Reserved
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    Eda2f1axw Level1

    Uploaded by

    Yi-Sin Lin - OXF.Student
    2 views6 pages

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    eda2f1axw_level1

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    2 views6 pages

    Eda2f1axw Level1

    Uploaded by

    Yi-Sin Lin - OXF.Student

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 6

    Edexcel AL Mathematics: Functions

    Section 1: Functions, graphs and transformations


    Exercise level 1 solutions
    1. (a) (i) The mapping is one-to-many.
    (ii) The mapping is not a function.

    (b) (i) The mapping is one-to-one.


    (ii) The mapping is a function.

    (c) (i) The mapping is many-to-many.


    (ii) The mapping is not a function.

    (d) (i) The mapping is many-to-one.


    (ii) The mapping is a function.

    2. (a)
    A B C

    (b) A is many-to-many
    B is one-to-one
    C isone-to-many

    (c) B is a function, A and C are not functions

    3. (a) f( x ) = 1− 3x where x  0
    The range is f( x )  1.

    (b) f( x ) = x 2 where x 

    Edexcel AL Maths: Functions 1 © MEI 22/03/24


    Exercise level 1 solutions page 1 of 6 integralmaths.org
    The range is f( x )  0 .

    1
    (c) f( x ) = where −1  x  1
    1+ x 2
    The largest possible value of f( x ) is when x = 0 , where f( x ) = 1 .
    The smallest possible value of f( x ) is when x = 1, where f( x ) = 21 .
    The range is 1
    2
     f( x )  1.

    4. (a) f( x )  +
    , f( x )  9

    (b) f( x )  , − 9  f( x )  21

    (c) f( x )  , − 1  f( x )  1

    (d) f( x )  , f( x )  0

    (e) f( x ) 

    (f) f( x )  , 0  f( x )  1

    5. (a) y = f( x + 2)

    This curve is obtained from the curve y = f ( x) by a translation of 2 units to the left.

    The turning point is (-1, 2).

    (b) y = f(3x )

    Edexcel AL Maths: Functions 1 © MEI 22/03/24


    Exercise level 1 solutions page 2 of 6 integralmaths.org
    1
    This curve is obtained from the curve y = f ( x) by a stretch, scale factor 3
    parallel to the x-axis.

    The turning point is ( 31 , 2).

    (c) y = f( x − 1) + 2

    1
    This curve is obtained from the curve y = f ( x) by a translation through  .
     2

    The turning point is (2, 4).

    (d) y = f( − x )

    This curve is obtained from the curve y = f ( x) by a reflection in the y-axis.

    The turning point is (-1, 2).

    Edexcel AL Maths: Functions 1 © MEI 22/03/24


    Exercise level 1 solutions page 3 of 6 integralmaths.org
    (e) y = −2f( x )

    This curve is obtained from the curve y = f ( x) by a reflection in the x-axis and a stretch scale factor 2
    parallel to the y-axis.

    The turning point is (1, -4).

    (f) y = f( 21 x − 1)

    This curve is obtained from the curve y = f ( x) by a translation of 1 unit to the right followed by a stretch,
    scale factor 2, parallel to the x-axis.

    The turning point is (4, 2).

    Edexcel AL Maths: Functions 1 © MEI 22/03/24


    Exercise level 1 solutions page 4 of 6 integralmaths.org
    6. (a)

    3
    A translation through   maps the curve y = f ( x) to the curve y = f ( x − 3) − 1 .
     −1 

    The curve y = x 2 is mapped to the curve


    y = ( x − 3)2 − 1
    = x2 − 6x + 9 − 1
    = x2 − 6x + 8

    (b)

    A stretch parallel to the x-axis, scale factor 1


    2
    maps the curve y = f ( x) to the curve y = f (2 x) .

    The curve y = x 2 is mapped to the curve


    y = (2 x )2
    = 4x2

    (c)

    A reflection in the y-axis maps the curve y = f ( x) to the curve y = f (− x) .

    The curve y = x 2 is mapped to the curve


    y = ( − x )2
    = x2

    (d)

    A stretch parallel to the y-axis, scale factor 3 maps the curve y = f ( x) to the curve y = 3f ( x) .

    Edexcel AL Maths: Functions 1 © MEI 22/03/24


    Exercise level 1 solutions page 5 of 6 integralmaths.org
    The curve of y = x 2 is mapped to the curve y = 3x 2

    (e)

     −2 
      maps the curve y = x to the curve y = ( x + 2)
    2 2
    A translation through
     0
    A reflection in the x-axis maps the curve y = ( x + 2) to the curve y = −( x + 2) .
    2 2

    y = −( x + 2)2
    = −( x 2 + 4 x + 4)
    = −x2 − 4x − 4

    (f)

    A stretch parallel to the y-axis, scale factor 2 maps the curve y = x to the curve y = 2 x .
    2 2

    1
      maps curve y = 2 x to the curve y = 2( x − 1) 2 + 2
    2
    A translation through
     
    2
    A reflection in the y-axis maps the curve y = 2( x − 1) + 2 to the curve y = 2(− x − 1) + 2 .
    2 2

    y = 2( − x − 1)2 + 2
    = 2( x 2 + 2 x + 1) + 2
    = 2x 2 + 4 x + 2 + 2
    = 2x 2 + 4 x + 4

    Edexcel AL Maths: Functions 1 © MEI 22/03/24


    Exercise level 1 solutions page 6 of 6 integralmaths.org

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