优优班--学霸训练营 > 知识点挑题
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            • 1.

              已知点\((a,\dfrac{1}{2})\)在幂函数\(f\left( x \right)=(a-1){{x}^{a}}\)的图象上,则函数\(f\left( x \right)\)是\((\)    \()\)

              A.奇函数  
              B.偶函数  
              C.定义域内的减函数  
              D.定义域内的增函数
            • 2. 已知幂函数\(y=x^{m^{2}-2m-3}(m∈N^{*})\)的图象与\(x\)轴、\(y\)轴无交点且关于原点对称,则\(m=\) ______ .
            • 3.

              已知函数\(f(x)=(m^{2}-m-5)x^{m}\)是幂函数,且在\(x∈(0,+∞)\)上为增函数,则实数\(m\)的值是\((\)  \()\)

              A.\(-2\)                           
              B.\(4\)

              C.\(3\)                                                      
              D.\(-2\)或\(3\)
            • 4.

              已知函数\(f(x)=x{\,\!}^{ \frac{1}{2}} \),则\((\)  \()\)

              A.\(∃x_{0}∈R\),\(f(x_{0}) < 0\)

              B.\(∀x∈[0,+∞)\),\(f(x)\geqslant 0\)

              C.\(∃x_{1}\),\(x_{2}∈[0,+∞)\),\( \dfrac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} < 0\)

              D.\(∀x_{1}∈[0,+∞)\),\(∃x_{2}∈[0,+∞)\),\(f(x_{1}) > f(x_{2})\)
            • 5.
              幂函数\(f(x)=(m^{2}-2m+1)x^{2m-1}\)在\((0,+∞)\)上为增函数,则实数\(m\)的值为\((\)  \()\)
              A.\(0\)
              B.\(1\)
              C.\(2\)
              D.\(1\)或\(2\)
            • 6.

              已知\(a∈\{-1,1,2,3\}\),则使函数\(y=x^{a}\)的值域为\(R\),且为奇函数的所有\(a\)的值为________.

            • 7.

              设函数\(y={{x}^{3}}\)与\(y={{\left( \dfrac{1}{2} \right)}^{x-2}}\)的图象的交点为\(\left({x}_{0},{y}_{0}\right) \),则\({{x}_{0}}\)所在的区间是      (    )

              A.\(\left(0,1\right) \)                   
              B.\(\left(1,2\right) \)                  
              C.\(\left(2,3\right) \)             
              D.\(\left(3,4\right) \)
            • 8.

              已知幂函数\(y=f(x)\)的图像过点\((2,\sqrt{2})\),则\(f(9)=\)________.

            • 9.
              已知幂函数\(y=f(x)\)的图象过点\((3, \sqrt {3})\),则\(f(9)=(\)  \()\)
              A.\(3\)
              B.\(-3\)
              C.\(- \sqrt {3}\)
              D.\( \sqrt {3}\)
            • 10. 幂函数\(y=f(x)\)的图象经过点\((2,8)\),则满足\(f(x)=27\)的\(x\)的值是 ______ .
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