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
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.
\(g(x) = \frac{3}
{x}\)
\(g(x) = -\frac{3}
{x}\)
\(g(x)= -\frac{1}
{x}\)
\(g(x) = \frac{2}
{x}\)
9000008008
Level:
C
Given the functions
\[
\text{$f(x) = -\frac{2}
{x}$ and $g(x)= \frac{k}
{x}$}
\]
find the value of the parameter \(k\in \mathbb{R}\setminus \{0\}\)
which ensures
\[
g(2) = 2f(-2).
\]
\(4\)
\(2\)
\(- 1\)
\(- 2\)
9000008005
Level:
A
Given the function \(f(x)= -\frac{10}
{x} \),
evaluate \(f(-5)\cdot f(2)\).
\(- 10\)
\(2.5\)
\(1\)
\(2.5\)
9000003107
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = -2 + \frac{1}
{x+1}\)
\(y = 2 + \frac{1}
{x+1}\)
\(y = 2 + \frac{1}
{x-1}\)
\(y = -2 + \frac{1}
{x-1}\)
9000003108
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = -2 - \frac{1}
{x-1}\)
\(y = -1 - \frac{1}
{x-2}\)
\(y = -2 + \frac{1}
{x-1}\)
\(y = 1 - \frac{1}
{x-2}\)
9000002901
Level:
B
Find the domain of the function \(f\colon y = \frac{1}
{x-2} + 1\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\)
9000002903
Level:
B
In the following list identify a point which is on the graph of the function
\(f(x) = \frac{3}
{x} - 5\).
\(A = \left [-6;-\frac{11}
{2} \right ]\)
\(A = \left [-1;-2\right ]\)
\(A = \left [-3;-\frac{5}
{2}\right ]\)
\(A = \left [\frac{1}
{2};-1\right ]\)
9000002906
Level:
B
Find the domain of the function
\(f(x) = - \frac{3}
{x-1} - 2\) if we have to ensure
that the range of \(f\)
is \((-1;1] \).
\((-2;0] \)
\([ - 2;0)\)
\((0;2] \)
\((0;4)\)
9000003101
Level:
A
Identify a possible analytic expression for the function graphed in the picture.
\(y = \frac{1}
{2x}\)
\(y = \frac{2}
{x}\)
\(y = -\frac{2}
{x}\)
\(y = -\frac{1}
{2x}\)