Rational functions

9000007702

Level: 
B
Identify a correct statement which concerns the function \(f(x) = \frac{1} {-x+2}\).
None of the statements above is true.
The function \(f\) is an increasing function.
The function \(f\) is bounded below.
The function \(f\) has a maximum at \(x = 2\).
The function \(f\) is decreasing on \((2;\infty )\).

9000007707

Level: 
B
Identify a correct statement which concerns the function \(f(x) = 2 -\frac{1} {x}\).
None of the statements above is true.
The function \(f\) is bounded above.
The function \(f\) is an even function.
The function \(f\) is a bounded function.
The function \(f\) is an odd function.

9000007709

Level: 
B
Identify a correct statement which concerns the function \(f(x) = -\frac{5} {x} - 3\).
None of the statements above is true.
The function \(f\) is bounded above.
The function \(f\) is an even function.
The function \(f\) is a decreasing function on \((0;\infty )\).
The function \(f\) is an odd function.

9000014201

Level: 
B
Find intersection points of the graph of the rational function \( f(x) = \frac{2x - 3} {x - 2} \) with \(y\)-axis.
\(Y = \left [0; \frac{3} {2}\right ]\)
\(Y = \left [\frac{3} {2};0\right ]\)
\(Y _{1} = \left [0; \frac{3} {2}\right ]\text{ and }Y _{2} = \left [\frac{3} {2};0\right ]\)
\(Y = \left [2;2\right ]\)

9000014203

Level: 
B
Which of the statements from the following list is true for the function \(f(x) = -\frac{2} {x} + 1\)?
The function \(f\) is a one-to-one function.
The function \(f\) is an odd function.
The function \(f\) is an increasing function.
The graph of the function \(f\) is a hyperbola with branches in the second and fourth quadrant.

9000014206

Level: 
B
Find the domain \(\mathrm{Dom}(f)\) and range \(\mathop{\mathrm{Ran}}(f)\) of the function \(f(x) = \frac{2+x} {x+4}\).
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;-4)\cup (-4;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;4)\cup (4;\infty ), \\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;1)\cup (1;\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;2)\cup (2;\infty ),\\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;4)\cup (4;\infty ) \end{align*}
\begin{align*} \mathrm{Dom}(f) &= (-\infty ;4)\cup (4;\infty ), \\ \mathop{\mathrm{Ran}}(f) &= (-\infty ;2)\cup (2;\infty ) \end{align*}