2100001702
Level:
B
Identify which of the graphs represents a part of the function \(f(x) = \sqrt[3]{x} \).
Power and radical functions
2110014803
Level:
B
Identify which of the graphs represents a part of the function \( f(x)=-\sqrt{x} \).
9000021708
Level:
B
In the following list identify a function with a domain
\(\left (-\infty ; \frac{1}
{2}\right )\).
\(f(x)= \sqrt{ \frac{10}
{2-4x}}\)
\(f(x)= \sqrt{\frac{2-4x}
{10}} \)
\(f(x) = \sqrt{2 - 4x}\)
\(f(x) = \sqrt{\frac{2-4x}
{3x}} \)
9000025804
Level:
B
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 1)(x + 2)(x - 3)
\]
The function \(f\)
is positive on \(I_{1} = (-2;-1)\)
and \(I_{2} = (3;\infty )\).
The function \(f\)
is an increasing function (in its whole domain).
The function is decreasing only on
\(I = (-1;3)\).
The function is decreasing on \(I_{1} = (-\infty ;-2)\)
and \(I_{2} = (3;\infty )\).
1003101101
Level:
C
Find the true statement about the function \( f(x)=\left|x^3+1\right| \).
The function \( f \) has the minimum at \( x=-1 \).
The function \( f \) has the minimum at \( x=0 \).
The function \( f \) has the minimum at \( x=1 \).
The function \( f \) has no minimum.
1003159101
Level:
C
Choose the function that describes the dependence of a cube volume \( V \) on the length of its space diagonal \( u \).
\( V=\frac{\sqrt3\cdot u^3}9;\ u\in(0;\infty) \)
\( V=u^3;\ u\in(0;\infty) \)
\( V=\frac{u^3}3;\ u\in(0;\infty) \)
\( V=27u^3;\ u\in(0;\infty) \)
1003159201
Level:
C
The 3D printer prints a solid \( 5 \) centimetre cube in \( 2 \) hours. The printer can print the cube with the maximum edge length of \( 20\,\mathrm{cm} \). Suppose the printing time is directly proportional to the cube volume. Choose the function that describes the dependence of the number \( n \) of cubes printed in \( 1 \) day on the printed cube edge length \( a \), which is specified in centimetres. Neglect time needed for using the printer.
\( n=1500a^{-3};\ a\in(0;20] \)
\( n=60a^{-1};\ a\in(0;20] \)
\( n=300a^{-2};\ a\in(0;20] \)
\( n=2.4a;\ a\in(0;20] \)
1103082706
Level:
C
Identify the graph of the function \( f(x)=\sqrt{|-x|};\ x\in [-9;9] \).
2010014804
Level:
C
Find the true statement about the function \( f(x)=\left|x^4-1\right| \).
The function \( f \) has the minima at \( x=-1 \) and \( x=1 \).
The function \( f \) has no minimum.
The function \( f \) has the minimum at \( x=0 \).
The function \( f \) has the minima at \( x=-1 \), \(x=0\) and \( x=1 \).
2010014805
Level:
C
Choose the function that describes the dependence of a cube surface \( S \) on the length of its space diagonal \( u \).
\( S=2u^2;\ u\in(0;\infty) \)
\( S=6u^2;\ u\in(0;\infty) \)
\( S=3u^2;\ u\in(0;\infty) \)
\( S=18u^2;\ u\in(0;\infty) \)