2100005409
Level:
B
Which of the graphs is the graph of the function \(f(x)=\mathrm{tg}\,\left(x+\frac{\pi}{4}\right)\)?
Sine, cosine, tangent and cotangent
9000004801
Level:
B
In the following list identify an even function.
\(y =\cos x\)
\(y =\sin x\)
\(y =\mathop{\mathrm{tg}}\nolimits x\)
\(y =\mathop{\mathrm{cotg}}\nolimits x\)
9000004807
Level:
B
In the following list identify a bounded function.
\(y =\sin x\)
\(y =\mathop{\mathrm{tg}}\nolimits x\)
\(y =\mathop{\mathrm{cotg}}\nolimits x\)
\(y = -\mathop{\mathrm{tg}}\nolimits x\)
9000033801
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(m\colon y =\cos x\)?
\(4\pi \)
\(\pi \)
\(5\pi \)
\(3\pi \)
9000033802
Level:
B
Which of the numbers in the list is a period (not necessarily the smallest period) of the
function \(n\colon y =\mathop{\mathrm{tg}}\nolimits x\)?
\(3\pi \)
\(\frac{\pi }{2}\)
\(- \frac{\pi } {2}\)
\(\frac{3\pi }
{2}\)
9000033803
Level:
B
In the following list identify a true statement about the function
\(f(x) =\sin x\), where
\(x\in \left [ -\frac{\pi }{2}; \frac{\pi } {2}\right ] \).
The function \(f\)
is increasing.
The function \(f\)
is decreasing.
The function \(f\)
is neither increasing nor decreasing.
The function \(f\) is non-increasing.
9000033804
Level:
B
In the following list identify a true statement for the function
\(g\colon y =\sin x\),
\(x\in [ - 2\pi ;-\pi ] \).
The function \(g\)
is neither increasing nor decreasing.
The function \(g\)
is increasing.
The function \(g\)
is decreasing.
9000033805
Level:
B
In the following list identify a true statement for the function
\(h\colon y =\mathop{\mathrm{cotg}}\nolimits x\),
\(x\in \left (-\frac{\pi }{2};0\right )\cup \left (0; \frac{\pi } {2}\right )\).
The function \(h\)
is neither increasing nor decreasing.
The function \(h\)
is increasing.
The function \(h\)
is decreasing.
9000033806
Level:
B
In the following list identify a true statement for the function
\(i\colon y =\mathop{\mathrm{tg}}\nolimits x\),
\(x\in \left ( \frac{\pi }{2}; \frac{3\pi }
{2}\right )\).
The function \(i\)
is increasing.
The function \(i\)
is decreasing.
The function \(i\)
is neither increasing nor decreasing.
9000033807
Level:
B
In the following list identify a true statement about the function
\(f(x) =\cos x\) on the
interval \(I = \left (-\frac{\pi }{2}; \frac{\pi } {2}\right )\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) does not have
a minimum or maximum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).