2110013903
Level:
A
The pictures show parts of graphs of even functions. Choose the picture showing the part of the graph of the function \(f(x)=\frac4{1+x^2}\).
A
2110013902
Level:
A
The pictures show parts of graphs of functions that are decreasing on the interval \([1;5]\). Choose the picture showing the part of the graph of the function \[f(x)=\frac{x+7}{x+1}.\]
2110013901
Level:
A
The pictures show parts of graphs of functions that are increasing on the interval \([1;5]\). Choose the picture showing the part of the graph of the function \[f(x)=\frac{5x-1}{x+1}.\]
2000019108
Level:
A
Determine the set of all values of the parameter \( a \in \mathbb{R} \setminus \{-2;2\}\) for which the equation has an infinite number of solutions.
\[
\frac{x-a}{2-a} = \frac{x+a}{2+a}
\]
\( \{0\}\)
\( \{-1\}\)
\( \{1\}\)
\(\emptyset\)
2000019107
Level:
A
Determine the set of all values of the real parameter \(a\) for which the equation has an infinite number of solutions.
\[
a^2x+1=x+a
\]
\( \{1\}\)
\( \{-1\}\)
\( \{0\}\)
\(\emptyset\)
2000019104
Level:
A
Consider the following equation with a parameter \( a\).
\[
5x-a=ax+4
\]
Choose the table that summarizes solutions of the equation according to the value of \(a\).
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline
a=5 & \emptyset \\
a \neq 5 & \left\lbrace\frac{a+4}{5-a}\right\rbrace
\\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline
a=5 & \mathbb{R} \\
a \neq 5 & \left\lbrace\frac{a+4}{5-a}\right\rbrace
\\\hline \end{array}\)
\(\begin{array}{cc} \hline \text{Parameter} & \text{Solution set}\\ \hline
a=5 & \mathbb{R}\\
a \neq 5 & \emptyset
\\\hline \end{array}\)
2000019103
Level:
A
Determine the set of all values of the parameter \( a \in \mathbb{R} \setminus \{3\} \) for which the given equation has no solution.
\[
\frac{5x-2}{a-3} = 4+ \frac{2x}3
\]
\(\left\{\frac{21}2\right\}\)
\(\left\{ \frac25\right\}\)
\( \{ -3 \}\)
\( \{0\}\)
2000019102
Level:
A
Determine the set of all values of the real parameter \( a \) for which the given equation has no solution.
\[
a^2x=x+a
\]
\(\{ -1;1\}\)
\(\{ -1;0;1\}\)
\( \{ 1 \}\)
\( \{ 0;1\}\)
2000018804
Level:
A
Given the function \(f(x) = -\frac{4}
{x}\),
find the function \(g\) such
that the graphs of \(f\)
and \(g\) are symmetric
about the \(y\)-axis.
\(g(x) = \frac{4}
{x}\)
\(g(x) =4
{x}\)
\(g(x) = -\frac{4}
{x}\)
\(g(x) = -{4}
{x}\)
2000018805
Level:
A
The test driver drove from Ostrava to Warsaw at an average speed of \(66\, \mathrm{km}/\mathrm{h}\) and the journey took him \(6\) hours. After him, the same route took several other drivers. (Each driver took a different driving time.) Choose the function giving the average speed \(v\) of each of these drivers as a function of the total driving time \(t\) from Ostrava to Warsaw.
\( v=\frac{396}t,\ \ t\in(0;\infty) \)
\( v=\frac{66}t,\ \ t\in(0;\infty) \)
\( v=66 t,\ \ t\in(0;\infty) \)
\( v=\frac{t}{396},\ \ t\in(0;\infty) \)