2010012303
Level:
A
Find the \(y\)-intercept
of the following function. \[f(x) = 6x^{2} +12x - 7.2\]
\([0;-7.2]\)
\([-7.2;0]\)
\([6;0]\)
There is no \(y\)-intercept.
A
2010012302
Level:
A
Find the intervals of monotonicity of the quadratic function
\(f(x) = -3x^{2} + 2\).
The function is increasing on \( (- \infty ;0 ] \)
and decreasing on \( [ 0;\infty ) \).
The function is increasing on \((-\infty;2) \)
and decreasing on \( ( 2;\infty) \).
The function is increasing on \(\left(-\infty;\frac23 \right] \)
and decreasing on \( \left[ \frac23;\infty\right) \).
The function is decreasing on its domain.
2010012301
Level:
A
Find the \(x\)-intercepts
of the function \(f(x)= 2x^{2} + 2x - 12\).
\([-3;0]\) and
\([2;0]\)
\([0;-12]\) and
\([2;0]\)
\([-3;2]\) and
\([-3;-2]\)
The function \(f\) does
not have \(x\)-intercepts.
2010012202
Level:
A
Find all the values of the real parameter \( a \) such that \( f(x)=ax^2+2 \) is increasing on \( (0;\infty) \).
\( a\in(0;+\infty) \)
\( a\in(-\infty;0) \)
\( a\in [ 2;+\infty) \)
\( a\in(-\infty;2 ] \)
2010012107
Level:
A
Find the solution set of the following equation.
\[ \frac2{5x^2-20}=0 \]
\(\emptyset\)
\(\left \{2\right \}\)
\( \left \{-2;2\right \}\)
\(\left \{-2\right \}\)
2010012106
Level:
A
Find the solution set of the following equation.
\[ \frac{4x^2-16}{x-2}=0 \]
\(\left \{-2\right \}\)
\( \left \{-2;2\right \}\)
\(\left \{2\right \}\)
\(\emptyset\)
2010012105
Level:
A
Find the solution set of the following equation.
\[ \frac{x^2-6x+9}{x-3}=0 \]
\(\emptyset\)
\(\left \{3\right \}\)
\( \left \{-3;3\right \}\)
\(\left \{-3\right \}\)
2010012104
Level:
A
Given graphs of the functions \( f(x)= x^2+x-6 \) and \( g(x) = x-2 \), find the domain of the equation \( \frac{x-2}{x^2+x-6}=1 \).
\(\mathbb{R}\setminus \left \{-3;2\right \}\)
\(\mathbb{R}\setminus \left \{-2;2\right \}\)
\(\mathbb{R}\setminus \left \{-3;-2;2\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)
2010012103
Level:
A
Find the domain of the expression.
\[
\frac{x^2-x-12}{3x^2+17x-6}
\]
\(\mathbb{R}\setminus \left \{-6;\frac{1}
{3}\right \}\)
\(\mathbb{R}\setminus \left \{-\frac{1}
{3};6\right \}\)
\(\left(-\frac13;6\right)\)
\(\left(-6;\frac13\right)\)
2010012102
Level:
A
Find the solution set of the following equation.
\[
\frac{9x +3}
{3x + 1} = 3
\]
\(\mathbb{R}\setminus \left \{-\frac{1}
{3}\right \}\)
\(\mathbb{R}\)
\(\{ 3\}\)
\(\emptyset\)