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.

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 \( \frac{x-2}{x^2+x-6}=1 \).
\(\mathbb{R}\setminus \left \{-3;2\right \}\)
\(\mathbb{R}\setminus \left \{-2;2\right \}\)
\(\mathbb{R}\setminus \left \{-3;-2;2\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)