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
\[
g(2) = 2f(-2).
\]
\(4\)
\(2\)
\(- 1\)
\(- 2\)
Rational Functions
9000007604
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{|x|+1}\right |\).
\(\mathbb{R}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1,1\}\)
\(\mathbb{R}\setminus \{ - 1,0,1\}\)
\(\mathbb{R}\setminus \{1\}\)
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.
\(g(x) = \frac{3}
{x}\)
\(g(x) = -\frac{3}
{x}\)
\(g(x)= -\frac{1}
{x}\)
\(g(x) = \frac{2}
{x}\)
9000007605
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{-|x|+1}\right |\).
\(\mathbb{R}\setminus \{ - 1,1\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1,0,1\}\)
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\)
9000003109
Level:
B
Identify the function that is graphed in the picture.
\(f(x) = \frac{x+3}
{x+2}\)
\(f(x) = \frac{x+2}
{x+1}\)
\(f(x) = \frac{x-2}
{x+1}\)
\(f(x) = -\frac{x+3}
{x+2}\)
9000003110
Level:
B
Identify the function that is graphed in the picture.
\(f(x) = \frac{2-x}
{1-x}\)
\(f(x) = \frac{x-2}
{x+1}\)
\(f(x) = -\frac{2-x}
{1-x}\)
\(f(x) = \frac{x-1}
{x+1}\)
9000002903
Level:
B
In the following list identify a point which is on the graph of the function
\(f(x) = \frac{3}
{x} - 5\).
\(A = \left [-6,-\frac{11}
{2} \right ]\)
\(A = \left [-1,-2\right ]\)
\(A = \left [-3,-\frac{5}
{2}\right ]\)
\(A = \left [\frac{1}
{2},-1\right ]\)
9000002904
Level:
B
Let by \(X\) and \(Y\) denote the intersection points of the graph of the function \(f(x) = - \frac{1}
{x-1} + 1 \)
with \(x\) and \(y\)-axis, respectively. Find coordinates of \(X\) and \(Y\).
\(X = [2,0]\),
\(Y = [0,2]\)
\(X = [1,0]\),
\(Y = [0,1]\)
\(X = [0,2]\),
\(Y = [2,0]\)
\(X = Y = [0,0]\)
9000002905
Level:
B
Find the range of the function \(f(x)= \frac{1}
{x-2} + 1\).
\((-\infty ,1)\cup (1,\infty )\)
\(\mathbb{R}\)
\((-\infty ,2)\cup (2,\infty )\)
\((-\infty ,-1)\cup (-1,\infty )\)
9000002902
Level:
B
The point \(A\) is on the
graph of the function \(f(x)= \frac{-10}
{x+5}\).
The \(x\)-coordinate
of the point \(A\)
is \(10\). Find the
\(y\)-coordinate
of the point \(A\).
\(-\frac{2}
{3}\)
\(\frac{2}
{3}\)
\(-\frac{1}
{5}\)
\(-\frac{1}
{3}\)