9000007501
Level:
B
The graph of the function
\[
f(x) = 1 + \frac{3}
{x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-2;1]\)
\(S = [3;1]\)
\(S = [1;3]\)
\(S = [1;-2]\)
\(S = [-2;3]\)
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 \(y = x\).
\(g(x) = \frac{5}
{x}\)
\(g(x) = \frac{1}
{x}\)
\(g(x)= -\frac{2}
{x}\)
\(g(x) = -\frac{5}
{x}\)
9000007603
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{2(x-2)}\right |\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{4\}\)
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\)
9000007502
Level:
B
The graph of the function
\[
f(x) = 2 - \frac{3}
{x - 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [2;2]\)
\(S = [-2;2]\)
\(S = [2;3]\)
\(S = [-2;3]\)
\(S = [2;0]\)
9000007604
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{|x|+1}\right |\).
\(\mathbb{R}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\setminus \{ - 1;0;1\}\)
\(\mathbb{R}\setminus \{1\}\)
9000007503
Level:
B
The graph of the function
\[
f(x) = 1 + \frac{1}
{2(x - 2)}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [2;1]\)
\(S = [1;1]\)
\(S = [1;2]\)
\(S = [-1;1]\)
\(S = [2;2]\)
9000007605
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{-|x|+1}\right |\).
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1;0;1\}\)
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\)
9000007602
Level:
B
Find the domain of the function \(f(x) = 2 - \frac{3}
{x-2}\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2;2\}\)
\(\mathbb{R}\setminus \{ - 3\}\)
\(\mathbb{R}\)
9000007606
Level:
B
Find the range of the function \(f(x) = 1 + \frac{3}
{x+2}\).
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2;1\}\)
\([ 0;\infty )\)
\(\mathbb{R}\)
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 \((2;\infty )\).