9000013504
Level:
B
Simplify \(\sqrt{\root{4}\of{25}}\).
\(\root{4}\of{5}\)
\(\root{8}\of{5}\)
\(\root{4}\of{25}\)
\(\sqrt{5}\)
B
9000013507
Level:
B
Simplify \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
9000010601
Level:
B
Identify a function which has a domain
\([ - 3;1] \).
\(y = \sqrt{-x^{2 } - 2x + 3}\)
\(y = \sqrt{-x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } - 2x + 3}\)
\(y = \sqrt{\frac{x+3}
{x+1}}\)
\(y = \sqrt{\frac{x-1}
{x+3}}\)
9000010603
Level:
B
Identify a function which has a domain
\(\left (-\infty ;-\frac{3}
{2}\right ] \).
\(y = \sqrt{-2x - 3}\)
\(y = \sqrt{3x + 2}\)
\(y = -\sqrt{2 - 3x}\)
\(y = \sqrt{x + \frac{3}
{2}}\)
\(y = \sqrt{x^{2 } - 3x}\)
\(y = \frac{1}
{3x+2}\)
9000010604
Level:
B
Identify a function which has a domain
\([ - 3;5)\).
\(y = \sqrt{\frac{x+3}
{5-x}}\)
\(y = \sqrt{(x - 3)(x + 5)}\)
\(y = \sqrt{\frac{x-5}
{x+3}}\)
\(y = \sqrt{(x - 5)(x + 3)}\)
\(y =\log \frac{x+5}
{x-3}\)
\(y =\log \frac{x+3}
{x-5}\)
9000014203
Level:
B
Which of the statements from the following list is true for the function
\(f(x) = -\frac{2}
{x} + 1\)?
The function \(f\)
is a one-to-one function.
The function \(f\)
is an odd function.
The function \(f\)
is an increasing function.
The graph of the function \(f\)
is a hyperbola with branches in the second and fourth quadrant.
9000010505
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x^{3}} : \root{3}\of{x}
\]
\(\root{15}\of{x^{4}}\)
\(\root{5}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(\root{5}\of{x^{2}}\)
9000007506
Level:
B
The graph of the function
\[
f(x) = \frac{3x - 4}
{x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-2;3]\)
\(S = [3;2]\)
\(S = [0;-4]\)
\(S = [0;4]\)
\(S = [4;-2]\)
9000007507
Level:
B
The graph of the function
\[
f(x) = \frac{2x - 4}
{3x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = \left [-\frac{2}
{3}; \frac{2}
{3}\right ]\)
\(S = \left [-\frac{3}
{2}; \frac{2}
{3}\right ]\)
\(S = \left [\frac{2}
{3};-\frac{3}
{2}\right ]\)
\(S = \left [-\frac{2}
{3};-\frac{2}
{3}\right ]\)
\(S = \left [\frac{3}
{2}; \frac{3}
{2}\right ]\)
9000007508
Level:
B
The graph of the function
\[
f(x) = \frac{2x + 1}
{x + 2}
\]
is a hyperbola. Find the center of this hyperbola.
\(S = [-2;2]\)
\(S = [2;-2]\)
\(S = [2;2]\)
\(S = [-2;-2]\)
\(S = [-2;3]\)