Properties of Functions

1103030803

Level: 
A
There is a part of the graph of the function \( f(x)=x^3 \) in the picture. Identify which of the following statements is true.
The function \( f \) is increasing in the interval \( [ -1,1 ] \).
The function \( f \) is decreasing in the interval \( [ -1,1 ] \).
The function \( f \) is non-decreasing and it is not increasing in the interval \( [ -1,1 ] \).
The function \( f \) is non-increasing in the interval \( [ -1,1 ] \).

1103030802

Level: 
A
The function \( f \) is given by the graph. Identify which of the following statements is true.
The function \( f \) is neither increasing nor decreasing.
The function \( f \) is increasing.
The function \( f \) is non-decreasing.
The function \( f \) is increasing in the interval \( [ -4,1] \).

1003030801

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

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.

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 \( x= 9 \).

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 \( x=3 \).

1003019403

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