Properties of functions

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.

2000005101

Level: 
A
Which of the given tables can define a function \(f\)?
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&1 &4& -2&-3&-1&2 \\\hline f(x) &3&3&1&1&1&3\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&-4 &-2& 0&-2&4&6 \\\hline f(x) &1&1&1&2&1&1\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&1 &4& -2&-3&1&2 \\\hline f(x) &-5&1&-2&1&3&6\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&1 &2& -2&-3&1&2 \\\hline f(x) &-1&0&2&3&-1&-2\\ \hline\end{array}\)

2000005104

Level: 
A
Find the inverse function to the function given by listing the points \( [x;f(x)]\). \[ f= \{[1;2];[2;3];[3;4];[4;5];[5;6]\} \]
\( f^{-1}= \{[2;1];[3;2];[4;3];[5;4];[6;5]\} \)
\( f^{-1}= \{[-1;-2];[-2;-3];[-3;-4];[-4;-5];[-5;-6]\} \)
\( f^{-1}= \left\{\left[1;\frac{1}{2}\right];\left[\frac{1}{2};\frac{1}{3}\right];\left[\frac{1}{3};\frac{1}{4}\right];\left[\frac{1}{4};\frac{1}{5}\right];\left[\frac{1}{5};\frac{1}{6}\right]\right\}\)
\(f^{-1}\) does not exist

2010014501

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

2010014505

Level: 
A
The function \( f \) is given by the graph. Which of the statements about the domain and the range of the function \( f \) is true?
\( D(f) =[ -6;2); H(f)= [ -1;3]\)
\( D(f) =[ -1;3] ; H(f)= [ -6;2)\)
\( D(f) =(-6;2); H(f)= [ -1;3]\)
\( D(f) =[ -6;2); H(f)= [ -1;3)\)

2010014506

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 decreasing.
The function \( f \) is decreasing in the interval \( [ -4;1] \).
The function \( f \) is increasing.