9000007609
Level:
C
Find the range of the function \(f(x) = 1 + \left | \frac{1}
{|x|+1}\right |\).
\((1;2] \)
\(\mathbb{R}\setminus \{ - 1;1\}\)
\((0;\infty )\)
\((1;\infty )\)
\(\mathbb{R}\)
Rational Functions
9000007504
Level:
B
The graph of the function
\[
f(x) = \frac{3}
{-2(x + 3)} - 1
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-3;-1]\)
\(S = [3;-1]\)
\(S = [3;1]\)
\(S = \left [\frac{3}
{2};-1\right ]\)
\(S = \left [-\frac{3}
{2};-1\right ]\)
9000007610
Level:
C
Find the range of the function \(f(x) = 1 + \left | \frac{1}
{-|x|+1}\right |\).
\((1;\infty )\)
\(\mathbb{R}\setminus \{ - 1\}\)
\((0;\infty )\)
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\)
9000007505
Level:
B
The graph of the function
\[
f(x) = \frac{1}
{-x + 3} + 2
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [3;2]\)
\(S = [-3;2]\)
\(S = [1;2]\)
\(S = [2;3]\)
\(S = [3;1]\)
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.
9000007506
Level:
B
The graph of the function
\[
f(x) = \frac{3x - 4}
{x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-2;3]\)
\(S = [3;2]\)
\(S = [0;-4]\)
\(S = [0;4]\)
\(S = [4;-2]\)
9000008002
Level:
A
Consider the point \(A = [-1;-3]\) and
the function \(f(x) = \frac{k}
{x}\) with a nonzero
real parameter \(k\in \mathbb{R}\setminus \{0\}\). Identify
the value of the parameter \(k\)
which ensures that the point \(A\)
is on the graph of \(f\).
\(3\)
\(1\)
\(- 1\)
\(- 3\)
9000007507
Level:
B
The graph of the function
\[
f(x) = \frac{2x - 4}
{3x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = \left [-\frac{2}
{3}; \frac{2}
{3}\right ]\)
\(S = \left [-\frac{3}
{2}; \frac{2}
{3}\right ]\)
\(S = \left [\frac{2}
{3};-\frac{3}
{2}\right ]\)
\(S = \left [-\frac{2}
{3};-\frac{2}
{3}\right ]\)
\(S = \left [\frac{3}
{2}; \frac{3}
{2}\right ]\)
9000008003
Level:
A
Given the function \(f(x) = \frac{6}
{x}\),
solve the following equation.
\[
f(x) = 2
\]
\(3\)
\(2\)
\(- 2\)
\(- 3\)
9000007508
Level:
B
The graph of the function
\[
f(x) = \frac{2x + 1}
{x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-2;2]\)
\(S = [2;-2]\)
\(S = [2;2]\)
\(S = [-2;-2]\)
\(S = [-2;3]\)