Rational functions

1003118302

Level:

Find the true statement about the function $ f(x)=1-\frac2{0.5x-1};\ x\in[-3;1)\cup(2;6] $.

The function $ f $ has no maximum.

The function $ f $ has the maximum at $ x=6 $.

The function $ f $ has the minimum at $ x=-3 $.

The function $ f $ is bounded.

1003118303

Level:

Find the false statement about the function $ f(x)=\frac{4x+1}{3-2x};\ x\in[2;\infty) $.

The function $ f $ has no minimum.

The function $ f $ is increasing.

The function $ f $ has no maximum.

The function $ f $ is bounded.

1003123901

Level:

Given $ f(x)=\frac{2x+3}{x-5} $, find the true statement in the following list.

$ f(x)=2+\frac{13}{x-5} $

$ f(x)=2+\frac3{x-5} $

$ f(x)=2x+\frac3{x-5} $

$ f(x)=3+\frac{2x}{x-5} $

1003123902

Level:

Given $ f(x)=\frac{3x-2}{2x-3} $, find the false statement in the following list.

$ f(x)=\frac32-\frac2{2x-3} $

$ f(x)=\frac32+\frac5{4\left(x-\frac32\right)} $

$ f(x)=\frac32-\frac5{6-4x} $

$ f(x)=\frac32+\frac{\frac52}{2x-3} $

1003123903

Level:

Given $ f(x)=\frac{2x-1}{3x+2} $, find the true statement in the following list.

$ f(x)=\frac23-\frac7{9\left(x+\frac23\right)} $

$ f(x)=\frac23+\frac1{3\left(3x+2\right)} $

$ f(x)=\frac32-\frac{\frac73}{3x+2} $

$ f(x)=2-\frac1{3x+2} $

Let \[ \begin{aligned} f(x)&=-2-\frac5{3(x-1)}, \\ g(x)&=\frac{2x-\frac13}{1-x}, \\ h(x)&=\frac{1-6x}{3x-3}, \\ j(x)&=\frac5{3x-3}-2. \end{aligned} \] From the following list choose the false statement.

$ h=j $

$ f=g $

$ f=h $

$ g=h $

1003123905

Level:

Let \[ \begin{aligned} f(x)&=\frac{6x-5}{5-2x}, \\ g(x)&=-3-\frac5{x-2}, \\ h(x)&=-3-\frac5{x-2.5}, \\ j(x)&=\frac{3x-1}{2-x}. \end{aligned} \] From the following list choose the true statement.

$ j=g $

$ f=g $

$ j=h $

$ f=j $