9000007109
Level:
B
The picture shows a graph of a quadratic function and three points on the graph. In
the following list identify another point on the graph of the same quadratic
function.
\([2;3]\)
\([2;2]\)
\([2;4]\)
\([2;5]\)
B
9000003705
Level:
B
Solve the following exponential equation.
\[
3^{2x} - 12\cdot 3^{x} + 27 = 0
\]
\(x_{1} = 1;\ x_{2} = 2\)
\(x_{1} = 3;\ x_{2} = 9\)
\(x_{1} = -1;\ x_{2} = -2\)
\(x_{1} = -3;\ x_{2} = -9\)
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 \(Y\).
\(X = [2;0]\),
\(Y = [0;2]\)
\(X = [1;0]\),
\(Y = [0;1]\)
\(X = [0;2]\),
\(Y = [2;0]\)
\(X = Y = [0;0]\)
9000002901
Level:
B
Find the domain of the function \(f\colon y = \frac{1}
{x-2} + 1\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\)
9000003109
Level:
B
Identify the function that is graphed in the picture.
\(f(x) = \frac{x+3}
{x+2}\)
\(f(x) = \frac{x+2}
{x+1}\)
\(f(x) = \frac{x-2}
{x+1}\)
\(f(x) = -\frac{x+3}
{x+2}\)
9000002903
Level:
B
In the following list identify a point which is on the graph of the function
\(f(x) = \frac{3}
{x} - 5\).
\(A = \left [-6;-\frac{11}
{2} \right ]\)
\(A = \left [-1;-2\right ]\)
\(A = \left [-3;-\frac{5}
{2}\right ]\)
\(A = \left [\frac{1}
{2};-1\right ]\)
9000003110
Level:
B
Identify the function that is graphed in the picture.
\(f(x) = \frac{2-x}
{1-x}\)
\(f(x) = \frac{x-2}
{x+1}\)
\(f(x) = -\frac{2-x}
{1-x}\)
\(f(x) = \frac{x-1}
{x+1}\)
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 \((-1;1] \).
\((-2;0] \)
\([ - 2;0)\)
\((0;2] \)
\((0;4)\)
9000002905
Level:
B
Find the range of the function \(f(x)= \frac{1}
{x-2} + 1\).
\((-\infty ;1)\cup (1;\infty )\)
\(\mathbb{R}\)
\((-\infty ;2)\cup (2;\infty )\)
\((-\infty ;-1)\cup (-1;\infty )\)
9000003103
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = 1 -\frac{2}
{x}\)
\(y = -1 + \frac{2}
{x}\)
\(y = 1 + \frac{2}
{x}\)
\(y = -1 -\frac{2}
{x}\)