1003024905
Level:
B
Which of the following functions is bounded above?
\( f(x) = -3^{-x} \)
\( f(x) = \left(\frac13\right)^{-x} \)
\( f(x) = 3^x \)
\( f(x) = \left(\frac13\right)^x \)
B
1003024904
Level:
B
Which of the following functions is decreasing?
\( f(x)=\left(\frac15\right)^x \)
\( f(x)=-5^{-x} \)
\( f(x)=\left(\frac15\right)^{-x} \)
\( f(x)=5^x \)
1003024903
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( 0 < b < 1 \), find the correct statement.
Function \( f \) is increasing.
Function \( f \) is decreasing.
Function \( f \) is nonincreasing.
Function \( f \) is nondecreasing.
1003024902
Level:
B
Given the function \(f(x)=a\cdot b^x\), where \( a < 0 \) and \( b > 0 \), find the correct statement.
Function \( f \) is bounded above.
Function \( f \) is bounded below.
Function \( f \) is bounded.
Function \( f \) is unbounded.
1003024901
Level:
B
Given the increasing exponential function \(f(x)=a^x\), choose the correct statement about the base \(a\).
\(a > 1\)
\(a=1\)
\(a < 1\)
\( 0 < a < 1 \)
1003020702
Level:
B
Find the solution of the inequality.
\[
\sqrt{3x^2-x+7}\geq2
\]
\(x\in\mathbb{R}\)
\(x\in\emptyset\)
\(x\in\left(-\frac13;\frac73\right)\)
\(x\in\mathbb{R}\setminus\{2\}\)
1003020701
Level:
B
Find the solution of the inequality.
\[
\sqrt{-2x^2+x+5}\geq5
\]
\(x\in\emptyset\)
\(x\in[-1;5]\)
\(x\in\left(-\frac12;\frac52\right)\)
\(x\in\mathbb{R}\)
9000168709
Level:
B
Find the vertex of the hyperbola \(9x^{2} - 16y^{2} - 36x - 96y + 36 = 0\).
\([2;-6]\)
\([2;-7]\)
\([5;-3]\)
\([6;-3]\)
9000168708
Level:
B
Find the vertex of the hyperbola \(4x^{2} - 9y^{2} + 24x + 18y + 63 = 0\).
\([-3;3]\)
\([-3;4]\)
\([-6;1]\)
\([-5;1]\)
9000168707
Level:
B
Find the vertex of the hyperbola \(9x^{2} - 4y^{2} - 54x - 16y + 29 = 0\).
\([5;-2]\)
\([6;-2]\)
\([3;-4]\)
\([3;-5]\)