Rational functions

1003109502

Level:

Let $ f(x)=-\frac2x\text{, }x\in[-2;0)\cup(0;\infty) $. Find the true statement.

The function $ f $ is injective (one-to-one).

The function $ f $ has minimum at $ x=-2 $.

The range of $ f $ is $ [0;1) $.

The function $ f $ is odd.

1003109501

Level:

Let $ f(x)=-\frac1{2x} $. Find the false statement.

The function $ f $ is increasing.

The range of $ f $ is $ \left(-\infty;0\right)\cup\left(0;\infty\right) $.

The function $ f $ is odd.

The function $ f $ is not bounded.

1003030903

Level:

Identify which of the following functions is bounded below.

$ h(x)=\frac{2x-4}{x-2} $

$ m(x)=\frac{x^2-4}{x-2} $

$ g(x)=\frac{4-x^2}{x-2} $

$ f(x)= -\left|\frac{x^2-4}{x-2}\right| $

1103030902

Level:

A part of the graph of the function $ f(x)=\frac4x $ is shown in the picture. Identify which of the following statements is true.

The function $ g $ defined by $ g(x)=\left|f(x)\right| $ is bounded below.

The function $ f $ is bounded below.

The function $h$ defined by $ h(x)=-f(x) $ is bounded below.

The function $m$ defined by $ m(x)=f(x)+4 $ is bounded below.

1103102304

Level:

Function $ f $ is given completely by the graph. Which of the following statements is false?

$ f(x)=\frac{|x|}x,\ x\in[-5;0)\cup(0;5] $

$ f(x)=\left|\frac{|x|}x\right|,\ x\in[-5;0)\cup(0;5] $

$ f(x)=1,\ x\in[-5;0)\cup(0;5] $

$ f(x)=\frac{x}x,\ x\in[-5;0)\cup(0;5] $

1103082701

Level:

Function $ f $ is given completely by the graph. Identify which of the following statements is false.

$ f(x)=\frac1x;\ x\in[-2;-0.5] $

$ f(x)=\left|-\frac1x\right|;\ x\in[-2;-0.5] $

$ f(x)=\frac1{|x|} ;\ x\in[-2;-0.5] $

$ f(x)=-\frac1x;\ x\in[-2;-0.5] $

1003028402

Level:

Let $ f(x)=\frac{2x-4}{x^2-4} $. Which of the statements about the domain and the range of the function $ f $ is true?

$ -2\notin D(f) \wedge -2\in H(f) $

$ -2\in D(f) \wedge -2\notin H(f) $

$ -2\in D(f) \wedge -2\in H(f) $

$ -2\notin D(f) \wedge -2\notin H(f) $

1003028401

Level:

Let $ f(x)=\frac{3x-9}{x^2-3} $. Which of the statements about the domain and the range of the function $ f $ is true?

$ 3\in D(f) \wedge 3\in H(f) $

$ 3\in D(f) \wedge 3\notin H(f) $

$ 3\notin D(f) \wedge 3\in H(f) $

$ 3\notin D(f) \wedge 3\notin H(f) $

1003019402

Level:

Identify which of the given functions is neither even nor odd.

$ h(x) = \frac{x^3-7}{2x^2} $

$ f(x) = \frac{x^2+3}{3x^4} $

$ g(x) = \frac{5x^2-6}{x} $

$ m(x) = \frac{x^3}{2x^2+5} $

1003019401

Level:

Identify which of the given functions is even.

$ m(x)=\frac{x^4-3}{x^2} $

$ h(x)=\frac{x^3+2}{x^2} $

$ g(x)=\frac{x^2}{x+1} $

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

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