Question

函數(shù)y=

1

2x+1

的值域是

{y|y≠0}

．

Answer 1

分析：由于y=

1

2x+1

=

1

2(x+ 1 2 )

=

1 2

x+ 1 2

，結(jié)合反比例函數(shù)的值域及函數(shù)圖象的平移可求

解答：解：∵y=

1

2x+1

=

1

2(x+ 1 2 )

=

1 2

x+ 1 2

又∵y =

1 2

x

的圖象向左平移

1

2

可得y=

1 2

x+ 1 2

的圖象，且反比例函數(shù)y=

1 2

x

≠0
∴y=

1

2x+1

=

1

2(x+ 1 2 )

=

1 2

x+ 1 2

≠0
故答案為{y|y≠0}

點(diǎn)評：本題主要考查了反比例函數(shù)的值域的求解及函數(shù)圖象的平移，屬于基礎(chǔ)試題