优优班--学霸训练营 > 知识点挑题
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            • 1. 如图,在正方形\(ABCD\)中,\(AB=2\),点\(E\),\(F\)分别在边\(AB\),\(DC\)上,\(M\)为\(AD\)的中点,且\(\overrightarrow{ME}· \overrightarrow{MF}=0 \)\(∆MEF \)的面积的取值范围为      \((\)  \()\)

              A.\(\left[1, \dfrac{5}{4}\right] \)
              B.\(\left[1,2\right] \)
              C.\(\left[ \dfrac{1}{2}, \dfrac{5}{4}\right] \)
              D.\(\left[ \dfrac{1}{2}, \dfrac{3}{2}\right] \)
            • 2.

              已知函数\(f\left(x\right)=4{x}^{2}+kx-1 \)在区间\(\left[1,2\right] \)上是单调函数,则实数\(k\)的取值范围是

              A.\((-∞,-16]∪[-8,+∞) \)
              B.\(\left[-16,18\right] \)
              C.\(\left(-∞,-8\right)∪[-4,+∞) \)
              D.\(\left[-8,-4\right] \)
            • 3.

              已知函数\(f(x)=\left( \left. \dfrac{1}{3} \right. \right)^{ax^{2}-4x+3} \).

              \((1)\)若\(a=-1\),求\(f(x)\)的单调区间;

              \((2)\)若\(f(x)\)有最大值\(3\),求\(a\)的值.

            • 4.

              函数\(y={{\log }_{\frac{1}{3}}}(4+3x-{{x}^{2}})\)的一个单调增区间是(    )

              A.\(\left( -\infty ,\dfrac{3}{2} \right)\)
              B.\(\left[ \dfrac{3}{2},+\infty \right]\)
              C.\(\left( -1,\dfrac{3}{2} \right)\)
              D.\(\left[ \dfrac{3}{2},4 \right) \)
            • 5.

              函数\(f(x)=\sqrt{{{x}^{2}}-2x-8}\)的单调递增区间是(    )

              A.\(\left( -\infty ,-2 \right]\)
              B.\(\left( -\infty ,1 \right]\)
              C.\(\left[ 1,+\infty \right)\)
              D.\(\left[ 4,+\infty \right) \)
            • 6.

              若函数\(f(x)={a}^{{x}^{2}-2x+1} \)在\((1,3)\)上是减函数,则关于\(x\)的不等式\(a^{x} > 1\)的解集为\((\)  \()\)


              A.\(\left\{ \left. x|x > 1 \right. \right\}\)
              B.\(\{x|x < 1\}\)
              C.\(\left\{ \left. x|x > 0 \right. \right\}\)
              D.\(\{x|x < 0\}\)
            • 7.

              函数\(f(x)=\ln (x\)\(2\)\(-3x-4)\)的单调递增区间是____\(.\) 

            • 8. 已知函数\(f(x){=}\dfrac{a{⋅}2^{x}{+}b{+}1}{2^{x}{+}1}\)是定义域在\(R\)上的奇函数,且\(f(2){=}\dfrac{6}{5}\).
              \((1)\)求实数\(a\)、\(b\)的值;
              \((2)\)判断函数\(f(x)\)的单调性,并用定义证明;
              \((3)\)解不等式:\(f(\log{{ }}_{\frac{1}{2}}(2x{-}2){]+}f{[}\log_{2}(1{-}\dfrac{1}{2}x){]\geqslant }0\).
            • 9. 函数\(f(x)=\log \;_{ \frac {1}{2}}(x^{2}-4)\)的单调递增区间为\((\)  \()\)
              A.\((0,+∞)\)
              B.\((-∞,0)\)
              C.\((2,+∞)\)
              D.\((-∞,-2)\)
            • 10.

              \((1)\)已知幂函数\(y=f(x)\)的图象经过点\((2,4)\),则这个函数的解析式是______.


              \((2)\)已知\(\cos ( \dfrac{7π}{8} -α)= \dfrac{1}{5} \),则\(\cos ( \dfrac{π}{8} +α)=\)______.


              \((3)\)已知定义在\(R\)上的奇函数\(f(x)\)满足\(f(x+3)=-f(x)\),则\(f(9)=\)______.


              \((4)\)有下列叙述:

              \(①\)若\( \overset{⇀}{a} =(1,k)\),\( \overset{⇀}{b} =(-2,6)\),\( \overset{⇀}{a} /\!/ \overset{⇀}{b} \),则\(k=-3\);

              \(②\)终边在\(y\)轴上的角的集合是\(\{α|α= \dfrac{kπ}{2} ,k∈Z\}\);

              \(③\)已知\(f(x)\)是定义在\(R\)上的不恒为\(0\)的函数,若\(a\),\(b\)是任意的实数,都有\(f(a⋅b)=f(a)+f(b)\),则\(y=f(x)\)的偶函数;

              \(④\)函数\(y=\sin (x- \dfrac{π}{2} )\)在\([0,π]\)上是减函数;

              \(⑤\)已知\(A\)和\(B\)是单位圆\(O\)上的两点,\(∠AOB= \dfrac{2}{3} π\),点\(C\)在劣弧\(\overbrace {AB} \)上,若\( \overset{⇀}{OC} =x \overset{⇀}{OA} +y \overset{⇀}{OB} \),其中,\(x\),\(y∈R\),则\(x+y\)的最大值是\(2\);

              以上叙述正确的序号是______.

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