9000014802
Level:
A
Let \(f(x) = -x^{2} + 11x - 2\).
Which of the following statements is true?
\(f(-2) = -28\)
\(f(0) = 2\)
\(f(3.5) = 12.25\)
\(f\left (\frac{1}
{2}\right ) = \frac{15}
{4} \)
A
9000014801
Level:
A
Identify a point which is on the graph of the function
\(f(x) = 3x^{2} + 3x - 2\).
\(B = [2;16]\)
\(A = [0;3]\)
\(C = [-1;0]\)
\(D = [5;-8]\)
9000014810
Level:
A
Find the domain and range of the quadratic function
\(f\)
graphed in the picture.
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left (-\infty ;2\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2;\infty \right )
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left [ 0;\infty \right )&
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2;4\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left (-\infty ;0\right ] &
\\&\mathop{\mathrm{Ran}}(f) =\mathbb{R}
\\ \end{aligned}\)
9000019801
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
x^{3} - 6x^{2} + 9x = 0
\]
\(\left \{3\right \}\)
\(\emptyset \)
\(\left \{0;3\right \}\)
\(\left \{-3;3\right \}\)
9000019802
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
2x^{3} - 3x^{2} = 0
\]
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{2\right \}\)
\(\left \{0; \frac{3}
{2}\right \}\)
9000014807
Level:
A
Find the \(x\)-intercepts
of the function \(f(x)= 3x^{2} + 6x - 9\).
\([-3;0]\) and
\([1;0]\)
\([0;9]\) and
\([1;0]\)
\([-3;2]\) and
\([-3;-2]\)
The function \(f\) does
not have \(x\)-intercepts.
9000014808
Level:
A
Find the intervals of monotonicity of the quadratic function
\(f(x) = 2x^{2} + 3\).
The function is increasing on \(\left [ 0;\infty \right )\)
and decreasing on \(\left (-\infty ;0\right ] \).
The function is increasing on \(\left (3;\infty \right )\)
and decreasing on \(\left (-\infty ;3\right )\).
The function is increasing on \(\left [ -\frac{3}
{2};\infty \right )\)
and decreasing on \(\left (-\infty ;-\frac{3}
{2}\right ] \).
The function is increasing on its domain.
9000014809
Level:
A
Find the \(y\)-intercept
of the following function: \[f(x) = 10x^{2} - 18x - 6.3\]
\([0;-6.3]\)
\([10;0]\)
\([0.3;0]\)
There is no \(y\)-intercept.
9000019903
Level:
A
Identify a true statement related to the following matrix
\(A\).
\[
A = \left (\array{
-2& 3 & 10& 5 & -5\cr
6 & 11 & -7 & 2 & -3
\cr
-7& 15& -6& 2 & 4\cr
-8 & 1 & 13 & -5 & 0
} \right )
\]
\(A\) is
a \(4\times 5\) matrix
and \(a_{(3,\, 2)} = 15\).
\(A\) is
a \(4\times 5\) matrix
and \(a_{(2,\, 3)} = 15\).
\(A\) is
a \(5\times 4\) matrix
and \(a_{(3,\, 2)} = -7\).
\(A\) is
a \(5\times 4\) matrix
and \(a_{(3,\, 2)} = 15\).
9000010607
Level:
A
Identify a function which is one-to-one on the interval
\([ - 2;2] \).
\(f(x) = x^{3} - 2\)
\(f(x) = x^{2} - 2\)
\(f(x) = -x^{2} + 2\)
\(f(x) = x^{-2} + 2\)
\(f(x) = \frac{1}
{x} - 2\)
\(f(x) = x^{4}\)