2100005105
Level:
A
The pictures show graphs of different functions \(f\). For which of the graphed functions is \(D(f) = \{2;3;4;5;6\}\)?
Properties of Functions
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
2100005103
Level:
A
In which picture is the graph of an odd function?
2100005102
Level:
A
In which picture is the graph of an even function?
2000005101
Level:
A
Which of the given tables can define a function \(f\)?
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&1 &4& -2&-3&-1&2 \\\hline f(x) &3&3&1&1&1&3\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&-4 &-2& 0&-2&4&6 \\\hline f(x) &1&1&1&2&1&1\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&1 &4& -2&-3&1&2 \\\hline f(x) &-5&1&-2&1&3&6\\ \hline\end{array}\)
\(\begin{array}{|c|c|c|c|c|c|c|} \hline x&1 &2& -2&-3&1&2 \\\hline f(x) &-1&0&2&3&-1&-2\\ \hline\end{array}\)
2000002406
Level:
C
Which of the functions is one-to-one?
\( f(x) = x-3 \)
\( f(x) = |x+1|\)
\( f(x) = x^3-x \)
\( f(x) = x^2 \)
2000002405
Level:
B
Decide which of the functions is odd.
\( f(x) = \frac{5}{x} \)
\( f(x) = \frac{x^2}{x^2-4} \)
\( f(x) = \frac{x^2}{2-x} \)
\( f(x) =(x+1)^2 \)
2000002404
Level:
B
Decide which of the functions is even.
\( f(x) = -x^2 +3 \)
\( f(x) = \frac{x}{x^2} \)
\( f(x)=-2x^3 \)
\( f(x) = \frac{1}{x^2+3x} \)
2000002403
Level:
B
Find the domain of the function \( f(x)=\frac{1}{|x-3|}\).
\( \mathbb{R} \setminus \{3\} \)
\( \mathbb{R} \)
\( (3;\infty) \)
\( (-3;3) \)
2000002402
Level:
B
Find the domain of the function \( f(x)= \frac{x^2 -1}{(x+1)^2}\).
\( \mathbb{R} \setminus \{-1\} \)
\( (-1;\infty ) \)
\( (-\infty; -1) \cup (1;\infty) \)
\( [ -1; \infty) \)