Properties of functions

1003019403

Level: 
A
Suppose each of the following tables defines function \( f \) completely. Identify which of the tables represents an odd function.
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-5&-3& -2&0&2&3&5 \\\hline f(x) &2&-3&1&0&-1&3&-2\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x& -5 & -3 & -1 & 0 & 1 & 3 & 5 \\\hline f(x) & -5 & -3 & -1 & 1 & 1 & 3 & 5 \\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline f(x) & 2 & -3 &1 & 0 & 1 & -3 & 2\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\\hline f(x) & 2 & -3 & 1 & -1 & 3 & 2 & 4\\ \hline\end{array}\)

1003019501

Level: 
A
Suppose function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2& -1&0&1&2&3 \\\hline f(x) &2&-3&1&0&1&-2&2\\ \hline\end{array}\] Identify which of the following statements is true.
Function \( f \) has minimum at \( x= -2\) and maximum at \( x= -3\) and at \( x= 3\).
Function \( f \) has minimum at \( x= -3\) and maximum at \( x= 2\).
Function \( f \) has minimum at \( x= -2\) and it has no maximum.
Function \( f \) has minimum at \( x= -3\) and maximum at \( x=3 \).

1003019502

Level: 
A
Suppose function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-2&5& 9&0&-8&2&4 \\\hline f(x) &2&-3&0&-7&-1&5&4\\ \hline\end{array}\] Identify which of the following statements is true.
Function \( f \) has minimum at \( x= 0 \) and maximum at \( x= 2 \).
Function \( f \) has minimum at \( x= 0 \) and maximum at \( x= 9 \).
Function \( f \) has minimum at \( x= -8 \) and maximum at \( x= 2 \).
Function \( f \) has minimum at \( x= -8 \) and maximum at \( x= 9 \).

1003028405

Level: 
A
Suppose the function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-2&-1& 0&1&2&3&4\\\hline y&0&1&0&2&3&5&4 \\\hline \end{array} \] Which of the following statements about the domain of the function \( f \) is true?
\( D(f)=\{-2; -1;0;1;2;3;4\} \)
\( D(f)=\{0;1;2;3;4;5\} \)
\( D(f)=\{-2;-1;0;1;2;3;4;5\} \)
\( D(f)=[-2;4] \)

1003028406

Level: 
A
Suppose the function \( f \) is given completely by the next table. \[ \begin{array}{|c|c|c|c|c|c|c|c|}\hline x&-3&-2&-1&0&1&2&3 \\\hline y&-4&4&-4&4&-4&4&-4 \\\hline \end{array} \] Which of the following statements about the range of the function \( f \) is true?
\( H(f)=\{-4; 4\} \)
\( H(f)=\{-3;-2;-1;0;1;2;3\} \)
\( H(f)=[-4;4] \)
\( H(f)=(-4;4) \)

1003030801

Level: 
A
Suppose each of the following tables defines functions completely. Identify which of the tables represents the decreasing function.
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x &-1 & -2 & 0 & -3 & 3 & 2 & 1 \\\hline f(x) & 3&4&-1&5&-5&-4&-3 \\\hline \end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x &3 & 2 & 1 & 0 & -1 & -2 & -3 \\\hline h(x) & 5&4&3&2&0&-1&-2 \\\hline \end{array} \)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x &-3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline g(x) & 3&2&1&0&3&2&1 \\\hline \end{array} \)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x &-1 & -2 & 0 & -3 & 3 & 2 & 1 \\\hline m(x) & 3&4&-3&5&-5&-4&-3 \\\hline \end{array}\)

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.

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.
\( f(-12)=3 \)
\( f(5)=1 \)
\( f(12)=3 \)
\( f(3.5)=0 \)

1103019503

Level: 
A
Function \( f \) is given by the graph. Identify which of the following statements is true.
Function \( f \) has minimum at \( x=0 \) and maximum at \( x=5 \).
Function \( f \) has minimum at \( x=-5 \) and maximum at \( x=5 \).
Function \( f \) has minimum at \( x=-1 \) and maximum at \( x=4 \).
Function \( f \) has neither minimum nor maximum.