Properties of functions

1003028407

Level: 
B
Paul went by car from Ostrava to Olomouc for a business trip. There he spent \( 50 \) minutes at the meeting and then he went back the same way. Paul covered the distance of \( 98\,\mathrm{km} \) from Ostrava to Olomouc in \( 64 \) minutes. The distance back he covered in \( 66 \) minutes. Suppose the recording of the travelled distance and the time spent on the business trip started when Paul left Ostrava. Dependence of this distance on the time describes the function \( s(t) \). Distance is in kilometres and time is in hours. Which of the following statements about the domain and the range of the function \( s \) is correct?
\( D(s)=[0;3] ; H(s)=[0;196] \)
\( D(s)=[0;196] ; H(s)=[0;3] \)
\( D(s)=[0;3] ; H(s)=[0;98] \)
\( D(s)=\left[0;\frac{13}6\right] ; H(s)=[0;196] \)

1003030807

Level: 
B
The function \( f(x) \) is increasing in the interval \( J \). Identify which of the following statements is false.
The function \( h(x) = -2 f(x) \) is increasing in the interval \( J \).
The function \( g(x) = 2 f(x) \) is increasing in the interval \( J \).
The function \( m(x) = f(x)+2 \) is increasing in the interval \( J \).
The function \( n(x) = f(x)-2 \) is increasing in the interval \( J \).

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?
\( g(x)=(-1)^{[x]} \)
\( f(x)=[2x]-2x \)
\( m(x)=3[x]-3x \)
\( h(x)=[x]-x \)