1003049304
Level:
B
Identify which of the following functions is increasing in the interval \( (-\infty; +2] \).
\( m(x)=-2|5-x|+1 \)
\( h(x)=|x|+2 \)
\( g(x)=-|x|-2 \)
\( f(x)=-|x+2| \)
B
1003049303
Level:
B
Let \( f(x)=-|x+3| \). Identify which of the following statements is false.
The function \( f \) is even.
The function \( f \) is decreasing in the interval \( [3; \infty) \).
The function \( f \) has maximum at \( x=-3 \).
The range of the function \( f \) is the interval \( (-\infty; 0] \).
1003049302
Level:
B
Let \( f(x)=2|-x|+1 \). Identify which of the following statements is false.
The function \( f \) is an injective (one-to-one) function.
The function \( f \) is increasing in the interval \( [0; \infty) \).
The function \( f \) has minimum at \( x=0 \).
The function \( f \) is non-increasing in the interval \( (-\infty; 0] \).
1003049301
Level:
B
Let \( f(x)=\frac12 (|x|-3) \). Identify which of the following statements is false.
The range of the function \( f \) is the interval \( [-3;\infty ) \).
The domain of the function \( f \) is the interval \( (-\infty;\infty) \).
The function \( f \) is even.
The function \( f \) is bounded below.
1003082404
Level:
B
Find the argument of the complex number \(4\left(\cos\frac{\pi}6-\mathrm{i}\cdot\sin\frac{\pi}6\right) \).
\( \frac{11\pi}6 \)
\( \frac{\pi}6 \)
\( \frac{5\pi}6 \)
\( \frac{7\pi}6 \)
1003082403
Level:
B
Find the argument of the complex number \( 2\left(\cos60^{\circ}-\mathrm{i}\cdot\sin60^{\circ}\right) \).
\( 300^{\circ} \)
\( 60^{\circ} \)
\( 120^{\circ} \)
\( 240^{\circ} \)
1003082402
Level:
B
Find the argument of the complex number \( 4\left(\cos\frac{\pi}3+\mathrm{i}\cdot\sin\frac{\pi}3\right) \).
\( \frac{\pi}3 \)
\( \frac{4\pi}3 \)
\( 4 \)
\( \frac{5\pi}3 \)
1003082401
Level:
B
Find the argument of the complex number \(\sqrt2\left(\cos160^{\circ}+\mathrm{i}\cdot\sin160^{\circ}\right) \).
\( 160^{\circ} \)
\( 200^{\circ} \)
\( \sqrt{2} \)
\( 340^{\circ} \)
1003048507
Level:
B
Let \( f \) be any periodic function. Identify which of the following statements is true.
The function \( f \) is not an injective (one-to-one) function.
\( D(f)=\mathbb{R} \).
The function \( f \) is bounded.
The function \( f \) is increasing.
1003048506
Level:
B
Identify which of the following functions has the smallest period.
\( f(x)=(\cos(2x) )^2 \)
\( h(x)=\sin\bigl(\frac{x}{2}\bigr) \)
\( m(x)=\mathrm{tg}\,\bigl(\frac{x}{2}\bigr) \)
\( g(x)=(\mathrm{cotg}\, x)^2 \)