1003030904
Level:
B
Identify which of the following functions is not bounded above.
\( m(x)=3-x^3 \)
\( h(x)=3 \)
\( g(x)=3-x^2 \)
\( f(x)= 3-\sqrt x \)
Properties of Functions
1103030901
Level:
A
The function \( f \) is given by the following graph. Identify which of the following statements is false.
The function \( f \) is not bounded below.
The function \( f \) is bounded below.
The function \( f \) is bounded above.
The function \( f \) is bounded.
1003048507
Level:
B
Let \( f \) be any periodic function. Identify which of the following statements is true.
The function \( f \) is not an injective (one-to-one) function.
\( D(f)=\mathbb{R} \).
The function \( f \) is bounded.
The function \( f \) is increasing.
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?
\( g(x)=(-1)^{[x]} \)
\( f(x)=[2x]-2x \)
\( m(x)=3[x]-3x \)
\( h(x)=[x]-x \)
1003048504
Level:
B
Identify which of the following functions is not periodic.
\( m(x)=(-2)^x,x\in\mathbb{Z} \)
\( h(x)=(-1)^x,x\in\mathbb{Z} \)
\( g(x)=-2,x\in\mathbb{R} \)
\( f(x)= 1^x,x\in\mathbb{R} \)
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.
1103048502
Level:
A
Let \( f \) be a periodic function with period \( 2.5 \). The diagram below shows a part of the graph of \( f \). Identify which of the following statements is false.
\( f(12.5)=-1 \)
\( f(3.5)=-1 \)
\( f(-2.75)=1 \)
\( f(11.25)=-0.5 \)
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.
\( f(-12)=3 \)
\( f(5)=1 \)
\( f(12)=3 \)
\( f(3.5)=0 \)
1103025602
Level:
A
Identify which of the graphs represents the function with the minimum at \( x=3 \).
1103025601
Level:
A
The function \( f \) is given by the graph. Which of the following statements is true?
The function \( f \) has a minimum and a maximum at every \( x \) of its domain.
The function \( f \) has the minimum at \( x=-6 \) and the maximum at \( x=3 \).
The function \( f \) has the maximum at \( x=3 \) and it has no minimum.
The function \( f \) has neither a minimum nor a maximum.