2010015105
Level:
B
Find the intersection points of the graph of the rational function \(f(x)=\frac{2x-6}{x+3}\) with \(x\)-axis.
\(X = \left [3; 0\right ]\)
\(X = \left [0; -2\right ]\)
\(X = \left [0; 3\right ]\)
\(X = \left [3; -3\right ]\)
Rational functions
2010015104
Level:
B
Find intersection points of the graph of the rational function \(f(x)=\frac{2x-6}{x+3}\) with \(y\)-axis.
\(Y = \left [0; -2\right ]\)
\(Y = \left [3; 0\right ]\)
\(Y = \left [0; -3\right ]\)
\(Y = \left [3; -3\right ]\)
2010015103
Level:
B
Identify the function that is graphed in the picture.
\(f(x) = \frac{1-2x}
{x-1}\)
\(f(x) = \frac{1+2x}
{x+1}\)
\(f(x) = \frac{x-2}
{x-1}\)
\(f(x) = \frac{x+2}
{x-1}\)
2010015102
Level:
B
Identify the function that is graphed in the picture.
\(f(x) = \frac{-x-4}
{x+3}\)
\(f(x) = \frac{-x+3}
{x-4}\)
\(f(x) = \frac{-x+3}
{x+1}\)
\(f(x) = \frac{-x-1}
{x+3}\)
2010015101
Level:
B
Let by \(X\) and \(Y\) denote the intersection points of the graph of the function \(f(x)=\frac{2}{x+3}-1\) with \(x\) and \(y\)-axis, respectively. Find coordinates of \(X\) and \(Y\).
\(X = [-1;0]\),
\(Y = \left[0;-\frac13\right]\)
\(X = [1;0]\),
\(Y = \left[0;\frac13\right]\)
\(X = \left[-\frac13;0\right]\),
\(Y = [0;-1]\)
\(X = [-3;0]\),
\(Y = [0;-1]\)
2010009905
Level:
A
Let \( f(x)=\frac{-3}{x} \). Find the false statement.
The function \(f\) is bounded above.
The range of \( f \) is \( \left(-\infty;0\right)\cup\left(0;\infty\right) \).
The function \( f \) is increasing on \( \left(-\infty;0\right) \).
The function \( h \) defined by \(h(x)=-f(x)\) is an odd function.
2010009904
Level:
C
A part of the graph of the function \( f(x)=\frac{-3}x \) is shown in the picture. Identify which of the following statements is true.
The function \( g \) defined by \( g(x)=-\left|f(x)\right| \) is bounded above.
The function \( m \) defined by \( m(x)=\left|f(x)\right| \) is bounded above.
The function \( h \) defined by \( h(x)=-f(x)\) is bounded below.
The function \( f \) is bounded below.
2010009903
Level:
B
Consider the function \(f(x) = \frac{6}
{x-1}-1 \).
Find all \(x\)
such that \(f(x) < 0\).
\(x\in \left (-\infty ;1\right )\cup (7;\infty )\)
\(x\in \left (-\infty ;-7\right )\cup (-1;\infty )\)
\(x\in (7;\infty)\)
\(x\in (-\infty;7)\)
2010009902
Level:
B
Consider the function \(f(x) = \frac{-1}
{x+2}-1 \).
Find all \(x\)
such that \(f(x) > 0\).
\(x\in (-3;-2)\)
\(x\in (-2;3)\)
\(x\in \left (-\infty ;-3\right )\cup (-2;\infty )\)
\(x\in \left (-\infty ;-2\right )\cup (3;\infty )\)
2010009901
Level:
B
Find the domain \(\mathrm{Dom}(f)\)
and range \(\mathop{\mathrm{Ran}}(f)\) of
the function \(f(x) = \frac{x-3}
{x+1}\).
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ;-1)\cup (-1;\infty ),\\
\mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty )
\end{align*}
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ;1)\cup (1;\infty ),\\
\mathop{\mathrm{Ran}}(f) &= (-\infty ;-1)\cup (-1;\infty )
\end{align*}
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ;3)\cup (3;\infty ),\\
\mathop{\mathrm{Ran}}(f) &= (-\infty ;-1)\cup (-1;\infty )
\end{align*}
\begin{align*}
\mathrm{Dom}(f) &= (-\infty ;-3)\cup (-3;\infty ),\\
\mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty )
\end{align*}