9000003108
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = -2 - \frac{1}
{x-1}\)
\(y = -1 - \frac{1}
{x-2}\)
\(y = -2 + \frac{1}
{x-1}\)
\(y = 1 - \frac{1}
{x-2}\)
B
9000003803
Level:
B
The function \(g\colon y =\log _{3}(x - 2)\)
is graphed in the picture. In the following list identify a false statement.
The function \(g\)
is a positive function.
The domain of the function \(g\)
is the interval \((2;\infty )\).
The function \(g\)
is not bounded.
The function \(g\)
is an increasing function.
The function \(g\)
has neither minimum nor maximum.
The graph of the function \(g\)
goes through \([5;1]\).
9000003604
Level:
B
Solve the following equation.
\[
10^{x} - 5^{x-1}\cdot 2^{x-2} = 950
\]
\(x = 3\)
\(x = 1\)
\(x = 2\)
\(x = 4\)
9000003805
Level:
B
Solve the following equation.
\[
\log x^{2}\cdot \log \sqrt{x} -\log \frac{1}
{x} = 2
\]
\(x_{1} = \frac{1}
{100}\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = 1\)
\(x_{1} = - \frac{1}
{100}\),
\(x_{2} = 10\)
\(x_{1} = -1\),
\(x_{2} = 2\)
9000003704
Level:
B
The function \(g(x) = 3 - 3^{x}\)
is graphed in the picture. In the following list identify one statement which is not
true.
The range of the function \(g\)
is \((-\infty ;3] \).
The function \(g\)
is neither odd nor even.
The function \(g\)
is decreasing on the domain.
The domain of the function \(g\)
is \((-\infty ;\infty )\).
The function \(g\)
is not bounded. It is bounded above.
All the values of the function \(g\)
are smaller than \(3\).
9000003602
Level:
B
Which values of the real parameter
\(p\) ensure that
the function \(f(x) = \left (\frac{p+1}
{p-3}\right )^{x}\)
is an increasing function?
\(p\in (3;\infty )\)
\(p\in \mathbb{R}\)
\(p\in \mathbb{R}\setminus \{3\}\)
\(p\in (-\infty ;-1)\cup (3;\infty )\)
9000003608
Level:
B
Solve the following equation.
\[
\frac{2}
{3}\cdot 9^{x+1} - 13\cdot 6^{x} + 24\cdot 4^{x-1} = 0
\]
\(1,\ -1\)
\(\frac{3}
{2},\ \frac{2}
{3}\)
\(\frac{1}
{2},\ -\frac{1}
{2}\)
\(\frac{3}
{2},\ -\frac{3}
{2}\)
9000003603
Level:
B
What are the values of the real \( a \), that satisfy inequality \(\left (\sqrt{3} -\sqrt{2}\right )^{2a+1} > \left (\sqrt{3} -\sqrt{2}\right )^{4-a}\)?
\(a < 1\)
\(a > 0\)
\(0 < a < 1\)
\(a > 1\)
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 \(Y\).
\(X = [2;0]\),
\(Y = [0;2]\)
\(X = [1;0]\),
\(Y = [0;1]\)
\(X = [0;2]\),
\(Y = [2;0]\)
\(X = Y = [0;0]\)