Properties of Functions

1003030906

Level: 
A
The function \( f \) has a maximum and has not a minimum. Identify which of the following statements is false, i.e. find the statement that is false for at least one of the functions that meet the given conditions.
The function \( f \) is not bounded above.
The function \( f \) is bounded below.
The function \( f \) is not bounded below.
The function \( f \) is not bounded.

1003048505

Level: 
B
Every real number \( x \) can be written as \( x=c+d \), where \( c \) is an integer and \( d\in[0; 1) \). Then \( c \) is called the integer part of \( x \) and is denoted by \( [x] \). Which of the following functions has the biggest primitive period?
\( g(x)=(-1)^{[x]} \)
\( f(x)=[2x]-2x \)
\( m(x)=3[x]-3x \)
\( h(x)=[x]-x \)

1103048503

Level: 
A
Let \( f \) be a periodic function with period \( 4 \). The diagram shows a part of the graph of \( f \). Identify which of the following statements is false.
The function \( f \) is an odd function.
The function \( f \) is increasing in the interval \( [14;15] \).
The function \( f \) has maximum at \( x=-5 \).
The function \( f \) is a bounded function.

1003048501

Level: 
A
Let \( f \) be a periodic function with period \( 5 \). The table below shows some input and corresponding output values of \( f \). \[\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -1.5 & -1 & 0 & 1 & 2 & 3 & 4 \\\hline f(x) & 0 & 4 & 1 & -1 & 3 & 2 & 4 \\\hline \end{array}\] Identify which of the following statements is false.
\( f(-12)=3 \)
\( f(5)=1 \)
\( f(12)=3 \)
\( f(3.5)=0 \)