2100021008
Level:
A
Which of the graphs is the graph of the following function?
\[f(x)=|x+2|+|2x+1|-|x-3|;\quad x\in[-4;1]\]
Linear functions with absolute values
2000021007
Level:
B
Which of the following functions is an odd function?
\(f(x)=|x-1|-|x+1|\)
\(g(x)=|x-1|+|x+1|\)
\(h(x)=-|x-1|-|x+1|\)
\(k(x)=|1-x|+|x-1|\)
2000021006
Level:
B
Which of the following functions is an even function?
\(f(x)=|1-x|+|x+1|\)
\(g(x)=|1-x|-|x+1|\)
\(h(x)=|1+x|+|x+1|\)
\(k(x)=|1-x|+|x-1|\)
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?
\(D(f)=\mathbb{R}\)
\(D(f)=[-3;\infty)\)
\(D(f)=[ -2;1]\)
\(D(f)=\mathbb{R}\setminus \left\{-2;1\right\} \)
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?
\(H(f)=[1;\infty)\)
\(H(f)=\mathbb{R}\)
\(H(f)=[-1;2]\)
\(H(f)=[-1;\infty)\)
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 \(x=-1\).
2000021002
Level:
B
In the picture, there is the graph of a function \(f\). Specify its formula.
\(f(x)=|x+1|-2x;\quad x\in[-2;3]\)
\(f(x)=|x+1|+2x;\quad x\in[-2;3]\)
\(f(x)=|x-1|-2x;\quad x\in[-2;3]\)
\(f(x)=|x-1|+2x;\quad x\in[-2;3]\)
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.
2100018602
Level:
C
Which of the following graphs is the graph of the function \(f(x)= \Bigl| \bigl| |x-1|-2\bigr|-3\Bigr|\); \(x \in [ -6;8]\)?
2000018601
Level:
C
Which of the following functions is increasing on the interval \([ -1;\infty)\)?
\( f(x)= 2\bigl| |x+3|-2\bigr|\)
\( g(x)= 2\bigl| |x-3|-2\bigr|\)
\( h(x)= -2\bigl| |x+3|-2\bigr|\)
\( k(x)= 2\bigl| |x-3|+2\bigr|\)