9000008007
Level:
A
Given the functions \(f(x) = -\frac{3}
{x}\)
and \(g(x) = 6\),
solve \(f(x) = g(x)\).
\(-\frac{1}
{2}\)
\(- 2\)
\(3\)
\(6\)
Rational functions
9000008009
Level:
A
Given the function \(f(x) = \frac{5}
{x}\),
find the function \(g\) such
that the graphs of \(f\)
and \(g\) are symmetric
about the line \(y = x\).
\(g(x) = \frac{5}
{x}\)
\(g(x) = \frac{1}
{x}\)
\(g(x)= -\frac{2}
{x}\)
\(g(x) = -\frac{5}
{x}\)
9000008010
Level:
A
Given the function
\(f\colon y = -\frac{3}
{x}\).
find the function \(g\) such
that the
graphs of \(f\)
and \(g\) are
symmetric
about the \(x\)-axis.
\(g(x) = \frac{3}
{x}\)
\(g(x) = -\frac{3}
{x}\)
\(g(x)= -\frac{1}
{x}\)
\(g(x) = \frac{2}
{x}\)
9000009908
Level:
A
Consider a function
\[
f(x) = \frac{-3}
{x}
\]
defined on the domain \(\mathrm{Dom}(f) =\mathbb{R}\setminus \{ - 1.0\}\).
Find the range of this function.
\(\mathbb{R}\setminus \{0.3\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\setminus \{ - 3.0\}\)
\(\mathbb{R}\)
9000009910
Level:
A
A body is deformed continuously in a machine press. The density
\(\rho \) is inversely proportional
to the volume \(V \) of the body,
i.e. there exists a constant \(k\)
such that
\[
\rho = \frac{k}
{V }.
\]
Find the constant \(k\)
(including the correct unit) if it is known that the density was
\(\rho = 25\: \frac{\mathrm{kg}}
{\mathrm{m}^{3}} \) when the body
had volume \(V = 2\, \mathrm{dm}^{3}\).
\(50\, \mathrm{g}\)
\(12.5\, \mathrm{g}\)
\(12.5\, \mathrm{m}\)
\(50\, \mathrm{m}\)
9100003201
Level:
A
Identify a possible graph of the function
\(f(x) = \frac{1}
{2x}\).
9100003202
Level:
A
Identify a possible graph of the function
\(f(x) = -\frac{2}
{x}\).
9100009902
Level:
A
The Newton's second law of motion
\[
F = m\cdot a
\]
states that the the acceleration \(a\)
of the body is directly proportional to the acting force,
\(F\).
The positive constant of this proportionality is the mass of the body,
\(m\). This
law can be also rewritten in the form of inverse proportionality between convenient
other quantities. Which of the graphs describes the Newton's second law properly,
assuming one of the quantities which appear in the Newton's law is constant?
9100009903
Level:
A
The resistance \(R\)
of a wire is a function of a material constant
\(\rho \), the length
\(l\) and the cross
section \(S\).
It can be computed from the formula
\[
R =\rho \cdot \frac{l}
{S}.
\]
Assuming two of the quantities are inversely proportional when the other two
quantities are constant, identify the graph which describes this relationship properly.
1003118301
Level:
B
Find the true statement about the function \( f(x)=-1+\frac3{2x-6} \).
The function \( f \) is decreasing on the interval \( (3;\infty) \).
The function \( f \) is decreasing on the interval \( (-3;\infty) \).
The function \( f \) is decreasing on the interval \( (-\infty;6) \).
The function \( f \) is decreasing on the interval \( (-1;\infty) \).