9000002901
Level:
B
Find the domain of the function \(f\colon y = \frac{1}
{x-2} + 1\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{0\}\)
\(\mathbb{R}\)
B
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 \((-1,1] \).
\((-2,0] \)
\([ - 2,0)\)
\((0,2] \)
\((0,4)\)
9000003103
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = 1 -\frac{2}
{x}\)
\(y = -1 + \frac{2}
{x}\)
\(y = 1 + \frac{2}
{x}\)
\(y = -1 -\frac{2}
{x}\)
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?
\(p\in (3,\infty )\)
\(p\in \mathbb{R}\)
\(p\in \mathbb{R}\setminus \{3\}\)
\(p\in (-\infty ,-1)\cup (3,\infty )\)
9000003104
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = -2 -\frac{1}
{x}\)
\(y = 2 + \frac{1}
{x}\)
\(y = -2 + \frac{1}
{x}\)
\(y = 2 -\frac{1}
{x}\)
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 \(3\).
9000003105
Level:
B
Identify a possible analytic expression for the function graphed in the picture.
\(y = \frac{1}
{x-2}\)
\(y = - \frac{1}
{x-2}\)
\(y = - \frac{1}
{x+2}\)
\(y = \frac{1}
{x+2}\)
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 \([5,1]\).
9000003706
Level:
B
In the following list identify an equation such that neither
\(x = 2\) nor
\(x = -2\) is the
solution of this equation.
\(\sqrt{2^{x}}\cdot \sqrt{3^{x}} = 36\)
\(0.25^{x} = 16\)
\(6^{-x} = \frac{1}
{36}\)
\(25^{x} = \left (\frac{1}
{5}\right )^{x^{2}
}\)
9000003705
Level:
B
Solve the following exponential equation.
\[
3^{2x} - 12\cdot 3^{x} + 27 = 0
\]
\(x_{1} = 1,\ x_{2} = 2\)
\(x_{1} = 3,\ x_{2} = 9\)
\(x_{1} = -1,\ x_{2} = -2\)
\(x_{1} = -3,\ x_{2} = -9\)