2110014806
Level:
C
Identify the graph of the function \( f(x)=-\sqrt{|x|};\ x\in [ -9;9] \).
Power and radical functions
2010014805
Level:
C
Choose the function that describes the dependence of a cube surface \( S \) on the length of its space diagonal \( u \).
\( S=2u^2;\ u\in(0;\infty) \)
\( S=6u^2;\ u\in(0;\infty) \)
\( S=3u^2;\ u\in(0;\infty) \)
\( S=18u^2;\ u\in(0;\infty) \)
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 \( x=1 \).
2110014803
Level:
B
Identify which of the graphs represents a part of the function \( f(x)=-\sqrt{x} \).
2010014802
Level:
B
In the following list identify a function with a domain
\(\left (\frac13;\infty \right)\).
\(f(x)= \sqrt{ \frac{5}
{9x-3}}\)
\(f(x)= \sqrt{ \frac{9x-3}
{5}}\)
\(f(x)= \sqrt{9x-3}\)
\(f(x)= \sqrt{ \frac{9x-3}
{3x}}\)
2010014801
Level:
B
Let \( f(x)=\sqrt[3]{(-x)^3} \) and \( g(x)=-x \). Identify which of the following statements is true.
\( f(x)=g(x) \)
\( f(-2)=-8 \)
\( g(-2)=-2 \)
\( f(x)=-g(x) \)
2010012406
Level:
A
Find the false statement about the function \( f(x)=(x-2)^4-3 \).
The function \( f \) is even.
The function \( f \) has the minimum at \( x=2 \).
The function \( f \) is bounded below.
The range of the function \( f \) is the interval \( [ -3;\infty) \).
2010012405
Level:
A
Find the true statement about the function \( f(x)=(x+1)^3-2 \).
The function \( f \) is an injective (one-to-one) function.
The function \( f \) is decreasing.
The function \( f \) is odd.
The function \( f \) has the minimum at \( x=-1 \).
2010012404
Level:
A
In the following list identify a decreasing function.
\(f \colon y =-x^{3}\)
\(f \colon y = x^{4}\)
\(f \colon y = -x^{4}\)
\(f \colon y = x^{-3}\)
\(f \colon y = -x^{2}\)
2010012403
Level:
A
Identify a function which is not one-to-one on the interval
\([ - 2;2 ] \).
\(f \colon y = x^{2}-2\)
\(f \colon y = x^{2}+4x\)
\(f \colon y = -x^{3}\)
\(f \colon y = (x - 2)^{2}\)
\(f \colon y = (x +2)^{2}\)
\(f \colon y = x^{3}-2\)