9000038903
Level:
B
Find the minimal value of the parameter
\(D\) which ensures
that the function \(f\colon y = D + 3\cdot \sin x\)
is nonnegative.
\(D = 3\)
\(D = -3\)
\(D = 6\)
\(D = -6\)
\(D = 1\)
No solution.
Sine, Cosine, Tangent, and Cotangent
9000038909
Level:
B
Consider the function \(f\colon y =\sin \left (\frac{x}
{2} + \frac{\pi }
{2}\right )\).
In the following list identify the function which has the same graph as the graph of the
function \(f\).
\(g\colon y =\cos \frac{x}
{2} \)
\(k\colon y =\cos \left (\frac{x}
{2} + \frac{\pi }
{2}\right )\)
\(b\colon y =\cos \left (\frac{x}
{2} - \frac{\pi }
{2}\right )\)
\(h\colon y =\cos \left (\frac{x}
{2} -\pi \right )\)
\(m\colon y =\cos 2x\)
9000038905
Level:
B
Identify the transformation which transforms the graph of the function
\(g(x) =\sin 3x\) to the graph
of the function \(f(x) =\sin (3x + 5)\).
Shift of graph of \(g\)
by \(\frac{5}
{3}\) of a
unit to the left.
Shift of graph of \(g\)
by \(5\)
units to the right.
Shift of graph of \(g\)
by \(5\)
units to the left.
Shift of graph of \(g\)
by \(3\)
units to the right.
Shift of graph of \(g\)
by \(3\)
units to the left.
Shift of graph of \(g\)
by \(\frac{5}
{3}\) of a
unit to the right.
9000038904
Level:
B
Consider function \(f\colon y =\sin x\) with domain
restricted to \(\mathop{\mathrm{Dom}}(f) =\mathbb{R}_{ 0}^{+}\). Identify the
function which is defined on \([ - 5,+\infty )\).
\(f(x + 5)\)
\(f(x - 5)\)
\(f(x) + 5\)
\(f(x) - 5\)
\(5\cdot f(x)\)
9000038906
Level:
B
Consider the function \(f\colon y =\mathop{\mathrm{tg}}\nolimits x\).
In the following list identify the nonnegative function.
None of the given functions is nonnegative.
\(A\cdot f(x)\),
where \(A\in (-\infty ,0)\)
\(A\cdot f(x)\),
where \(A\in (0,+\infty )\)
\(f(B\cdot x)\),
where \(B\in (0,+\infty )\)
\(f(x + C)\),
where \(C\in (-\infty ,0)\)
9000038907
Level:
B
Consider the function \(f(x) =\mathop{\mathrm{cotg}}\nolimits x\) with
domain restricted to the interval \(\mathop{\mathrm{Dom}}(f) = (0,\pi )\).
In the following list identify the function with domain
\(\left (0, \frac{\pi } {3}\right )\).
\(f(3\cdot x)\)
\(f(x - 3)\)
\(f(x + 3)\)
\(f\left (\frac{x}
{3} \right )\)
\(3\cdot f(x)\)
9000038908
Level:
B
Consider the function \(f\colon y =\mathop{\mathrm{tg}}\nolimits x\) with
domain restricted to the interval \(\mathop{\mathrm{Dom}}(f) = \left ( \frac{\pi }{2}, \frac{3\pi }
{2}\right )\).
In the following list identify the function with domain
\((0,\pi )\).
\(f\left (x + \frac{\pi } {2}\right )\)
\(\left ( \frac{\pi }{2}\right )\cdot f(x)\)
\(f\left (x - \frac{\pi } {2}\right )\)
\(f(x) + \frac{\pi } {2}\)
\(f(x) - \frac{\pi } {2}\)
9000038901
Level:
B
Consider the function \(f\colon y = A\cdot \sin (B\cdot x + C)\), with
real nonzero parameters \(A\),
\(B\) and
\(C\).
Which of the following operations makes the period of the function five times
smaller?
Increase \(B\) by
a factor \(5\).
Increase \(A\)
by a factor \(5\).
Decrease \(A\)
by a factor \(5\).
Decrease \(B\)
by a factor \(5\).
Increase \(C\)
by a factor \(5\).
Decrease \(C\)
by a factor \(5\).
9000038902
Level:
B
Consider the function \(f\colon y = A\cdot \sin (B\cdot x + C)\), with
real nonzero parameters \(A\),
\(B\) and
\(C\).
Which of the following operations makes the amplitude of the function five times
bigger?
Decrease \(A\)
by a factor \(5\).
Increase \(A\) by
a factor \(5\).
Increase \(B\)
by a factor \(5\).
Decrease \(B\)
by a factor \(5\).
Increase \(C\)
by a factor \(5\).
Decrease \(C\)
by a factor \(5\).
9000033809
Level:
B
Find the parity (odd/even) of the function
\(k\colon y = -\mathop{\mathrm{tg}}\nolimits x\).
The function \(k\)
is an odd function.
The function \(k\)
is an even function.
The function \(k\)
is neither an odd nor even function.