1003030804
Level:
B
Identify which of the following functions is decreasing in the interval \( [ 0;\infty ) \).
\( m(x)=-x^2 \)
\( h(x) = \frac1x \)
\( g(x) = -100+0.1x \)
\( f(x) = (-x)^2 \)
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.
\(\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x &-1 & -2 & 0 & -3 & 3 & 2 & 1 \\\hline f(x) & 3&4&-1&5&-5&-4&-3 \\\hline
\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x &3 & 2 & 1 & 0 & -1 & -2 & -3 \\\hline h(x) & 5&4&3&2&0&-1&-2 \\\hline
\end{array}
\)
\(\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x &-3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline g(x) & 3&2&1&0&3&2&1 \\\hline
\end{array}
\)
\(\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x &-1 & -2 & 0 & -3 & 3 & 2 & 1 \\\hline m(x) & 3&4&-3&5&-5&-4&-3 \\\hline
\end{array}\)
1103019504
Level:
A
Identify which of the graphs represents a function without a maximum.
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 \( x=3 \).
1103019404
Level:
A
Identify which of the given graphs is an even function graph.
1003019403
Level:
A
Suppose each of the following tables defines function \( f \) completely. Identify which of the tables represents an odd function.
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-5&-3& -2&0&2&3&5 \\\hline f(x) &2&-3&1&0&-1&3&-2\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x& -5 & -3 & -1 & 0 & 1 & 3 & 5 \\\hline f(x) & -5 & -3 & -1 & 1 & 1 & 3 & 5 \\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline f(x) & 2 & -3 &1 & 0 & 1 & -3 & 2\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\\hline f(x) & 2 & -3 & 1 & -1 & 3 & 2 & 4\\ \hline\end{array}\)