9000004809
Level:
B
In the following list identify a function which is bounded above.
\(f(x) = -(x - 2)^{2}\)
\(f(x) = x^{2}\)
\(f(x) = x^{2} - 3x\)
\(f(x) = (x - 3)^{2}\)
Properties of functions
9000010601
Level:
B
Identify a function which has a domain
\([ - 3;1] \).
\(y = \sqrt{-x^{2 } - 2x + 3}\)
\(y = \sqrt{-x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } - 2x + 3}\)
\(y = \sqrt{\frac{x+3}
{x+1}}\)
\(y = \sqrt{\frac{x-1}
{x+3}}\)
9000010602
Level:
B
Identify a function which has a domain
\((-\infty ;-2)\cup (2;\infty )\).
\(y = \sqrt{ \frac{1}
{x^{2}-4}}\)
\(y = \frac{1}
{x^{2}-4}\)
\(y = \sqrt{x^{2 } + 4}\)
\(y = \sqrt{x^{2 } - 2}\)
\(y = \sqrt{x^{2 } - 4}\)
\(y = \sqrt{ \frac{1}
{x^{2}-2}}\)
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
\([ - 3;5)\).
\(y = \sqrt{\frac{x+3}
{5-x}}\)
\(y = \sqrt{(x - 3)(x + 5)}\)
\(y = \sqrt{\frac{x-5}
{x+3}}\)
\(y = \sqrt{(x - 5)(x + 3)}\)
\(y =\log \frac{x+5}
{x-3}\)
\(y =\log \frac{x+3}
{x-5}\)
9000021808
Level:
B
Find the domain of the following function.
\[
f(x) = \sqrt{\frac{(x - 3)(x + 2)}
{(1 - x)(3 - x)}}
\]
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;3)\cup (3;\infty )\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2)\cup (1;3)\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;\infty )\)
\(\mathop{\mathrm{Dom}}(f) =[ -2;1)\cup (3;\infty )\)
9000033703
Level:
B
Find the domain of the following function.
\[
f\colon y = \frac{x}
{\sqrt{4x^{2 } - 9}}
\]
\(\left (-\infty ;-\frac{3}
{2}\right )\cup \left (\frac{3}
{2};\infty \right )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \left \{-\frac{3}
{2}; \frac{3}
{2}\right \}\)
\(\left (-\frac{3}
{2}; \frac{3}
{2}\right )\)
\(\left [ -\frac{3}
{2}; \frac{3}
{2}\right ] \)
\(\left (-\infty ;-\frac{3}
{2}\right ] \cup \left [ \frac{3}
{2};\infty \right )\)
1003030401
Level:
C
Suppose function \( f \) is given completely by the next table.
\[
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline f(x)&-1&0&1&2&3&4&5 \\\hline
\end{array}\]
Identify which of the following functions is the inverse of \( f \).
Function \( h \), which is given completely by the next table.
\(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-1&0&1&2&3&4&5 \\\hline h(x)&-3&-2&-1&0&1&2&3 \\\hline
\end{array}\)
Function \( m \), which is given completely by the next table.
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline m(x)&5&4&3&2&1&0&-1 \\\hline
\end{array}\)
Function \( g \), such that \( g(x)=x-2 \) for \( x\in[-1;5] \).
Function \( n \), such that \( n(x)=x+2 \) for \( x\in[-3;3] \).
1003030402
Level:
C
Suppose function \( f \) is given completely by the next table.
\[
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline f(x)&-1&2&-3&1&-2&3&2 \\\hline
\end{array}\]
Identify which of the following statements is true.
The inverse of \( f \) does not exist.
The inverse of \( f \) is function \( h \), which is given completely by the next table.
\(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-1&2&-3&1&-2&3&2 \\\hline h(x)&-3&-2&-1&0&1&2&3 \\\hline
\end{array}
\)
The inverse of \( f \) is function \( g \), which is given completely by the next table. \(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&-3&-2&-1&0&1&2&3 \\\hline g(x)&1&-2&3&-1&2&-3&-2 \\\hline
\end{array}\)
The inverse of \( f \) is function \( m \), which is given completely by the next table. \(
\begin{array}{|c|c|c|c|c|c|c|c|} \hline x&3&2&1&0&-1&-2&-3 \\\hline m(x)&1&-2&3&-1&2&-3&-2 \\\hline
\end{array}\)
1003030403
Level:
C
Identify which of the following functions is not an injective (one-to-one) function.
\( m(x)=|x-2|;\ x\in[-2; 3 ) \)
\( h(x)=x^3+3;\ x\in[-2;3) \)
\( g(x)=(x+2)^2;\ x\in[-2; 3) \)
\( f(x)= \frac{x+2}{x-3};\ x\in[-2; 3) \)