9000007610
Level:
C
Find the range of the function \(f(x) = 1 + \left | \frac{1}
{-|x|+1}\right |\).
\((1;\infty )\)
\(\mathbb{R}\setminus \{ - 1\}\)
\((0;\infty )\)
\(\mathbb{R}\setminus \{ - 1;1\}\)
\(\mathbb{R}\)
Rational Functions
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.
\(S = [-2;3]\)
\(S = [3;2]\)
\(S = [0;-4]\)
\(S = [0;4]\)
\(S = [4;-2]\)
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 \(Y\).
\(X = [2;0]\),
\(Y = [0;2]\)
\(X = [1;0]\),
\(Y = [0;1]\)
\(X = [0;2]\),
\(Y = [2;0]\)
\(X = Y = [0;0]\)
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.
\(f(x) = \frac{2-x}
{1-x}\)
\(f(x) = \frac{x-2}
{x+1}\)
\(f(x) = -\frac{2-x}
{1-x}\)
\(f(x) = \frac{x-1}
{x+1}\)
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 \(A\).
\(-\frac{2}
{3}\)
\(\frac{2}
{3}\)
\(-\frac{1}
{5}\)
\(-\frac{1}
{3}\)
9000002908
Level:
C
Find the intervals where the function
\(f(x) = \left |1 + \frac{1}
{x}\right |\) is an increasing
function. The function \(f\)
is graphed in the picture.
\([ - 1;0)\)
\((-\infty ;1] \)
\((-\infty ;0)\)
\((0;\infty )\)
9000002907
Level:
B
Identify a possible analytic expression for the function graphed in the
picture.
\(y = -2 + \frac{1}
{x+1}\)
\(y = - \frac{1}
{x+1} - 2\)
\(y = \frac{1}
{x+2} - 1\)
\(y = 2 + \frac{1}
{x+1}\)