1103162908
Level:
B
With aid of the given graph of a function \( f \), find all \( x \) so that \( |f(x)-2|=1 \).
\( x\in\{-4;-2\} \)
\( x\in\{-4;2\} \)
\( x\in\{-2;2\} \)
\( x\in\{-3\} \)
Functions with absolute values
1103162909
Level:
B
With aid of the graph of a function \( f \) find all \( x\), so that \( |f(x)|=3 \).
\( x\in\{-5;1\} \)
\(x\in \{1\} \)
\(x\in \{-2\} \)
\( x\in\{-5;5\} \)
2000021001
Level:
B
In the picture, there is the graph of a function \(f\). Which of the following statements is true?
The function \(f\) is bounded.
The function \(f\) has its maximum and has no minimum.
The function \(f\) is a one-to-one function and is decreasing.
The function \(f\) is an odd function and is bounded below.
2000021002
Level:
B
In the picture, there is the graph of a function \(f\). Specify its formula.
\(f(x)=|x+1|-2x;\quad x\in[-2;3]\)
\(f(x)=|x+1|+2x;\quad x\in[-2;3]\)
\(f(x)=|x-1|-2x;\quad x\in[-2;3]\)
\(f(x)=|x-1|+2x;\quad x\in[-2;3]\)
2000021003
Level:
B
Consider the function \(f(x)=|x+1|-2\). Which of the statements is true?
The function \(f\) has a minimum at the point \(x=-1\).
The function \(f\) has a minimum at the point \(x=-2\).
The function \(f\) has no minimum.
The function \(f\) has a maximum at the point \(x=-1\).
2000021004
Level:
B
Which of the given statements about the range \(H(f)\) of the function \(f(x)=|2-x|+|1+x|-2\) is true?
\(H(f)=[1;\infty)\)
\(H(f)=\mathbb{R}\)
\(H(f)=[-1;2]\)
\(H(f)=[-1;\infty)\)
2000021005
Level:
B
Which of the given statements about the domain \(D(f)\) of the function \(f(x)=3|x+2|-|x-1|\) is true?
\(D(f)=\mathbb{R}\)
\(D(f)=[-3;\infty)\)
\(D(f)=[ -2;1]\)
\(D(f)=\mathbb{R}\setminus \left\{-2;1\right\} \)
2000021006
Level:
B
Which of the following functions is an even function?
\(f(x)=|1-x|+|x+1|\)
\(g(x)=|1-x|-|x+1|\)
\(h(x)=|1+x|+|x+1|\)
\(k(x)=|1-x|+|x-1|\)
2000021007
Level:
B
Which of the following functions is an odd function?
\(f(x)=|x-1|-|x+1|\)
\(g(x)=|x-1|+|x+1|\)
\(h(x)=-|x-1|-|x+1|\)
\(k(x)=|1-x|+|x-1|\)
2010009202
Level:
B
Which of the following functions is bounded?
\( f(x)=|3+x|-|x| \)
\( g(x)=|3+x|+|x| \)
\( h(x)=|x-3|+|x| \)
\( m(x)=3-|x| \)