1003118304
Level:
C
Identify which of the following functions is bounded.
\( h(x)=\frac{3x-6}{2x-4} \)
\( f(x)=\frac{3x-6}{2x} \)
\( g(x)=3-\frac6{2x} \)
\( m(x)=\left|\frac{4x-3}{2x-6}\right| \)
Rational functions
1003118303
Level:
B
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.
1003118302
Level:
B
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.
1003118301
Level:
B
Find the true statement about the function \( f(x)=-1+\frac3{2x-6} \).
The function \( f \) is decreasing on the interval \( (3;\infty) \).
The function \( f \) is decreasing on the interval \( (-3;\infty) \).
The function \( f \) is decreasing on the interval \( (-\infty;6) \).
The function \( f \) is decreasing on the interval \( (-1;\infty) \).
1003109502
Level:
A
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:
A
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:
C
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:
B
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:
C
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:
C
Function \( f \) is given completely by the graph. Identify which of the following statements is false.
\( f(x)=\frac1x;\ x\in[-2;-0.5] \)
\( f(x)=\left|-\frac1x\right|;\ x\in[-2;-0.5] \)
\( f(x)=\frac1{|x|} ;\ x\in[-2;-0.5] \)
\( f(x)=-\frac1x;\ x\in[-2;-0.5] \)