1103099802
Level:
A
The function \( f(x)=\log_{\frac12} (x+3) \) is graphed below. Which of the following equations is the equation of the vertical asymptote of \( f \)?
\( x = -3 \)
\( x = 3 \)
\( y = -3 \)
\( y = 3 \)
A
1103099801
Level:
A
The function \( f(x)=\log_2(x+3) \) is graphed below. Find the vertical asymptote of \( f \).
\( x=-3 \)
\( x=3 \)
\( y=-3 \)
\( y=3 \)
1003030906
Level:
A
The function \( f \) has a maximum and has not a minimum. Identify which of the following statements is false, i.e. find the statement that is false for at least one of the functions that meet the given conditions.
The function \( f \) is not bounded above.
The function \( f \) is bounded below.
The function \( f \) is not bounded below.
The function \( f \) is not bounded.
1103030901
Level:
A
The function \( f \) is given by the following graph. Identify which of the following statements is false.
The function \( f \) is not bounded below.
The function \( f \) is bounded below.
The function \( f \) is bounded above.
The function \( f \) is bounded.
1003061306
Level:
A
Determine the relative position of the lines \( p\colon 2x-3y+7=0 \) and
\[ \begin{aligned} q\colon x& =2+t, \\
y& = -3t, \end{aligned} \]
where \( t\in\mathbb{R} \).
intersecting lines, \( p\cap q=\left\{\left[1;3\right]\right\} \)
identical lines, \( p=q \)
parallel different lines, \( p\parallel q;\ p\neq q \)
intersecting lines, \( p\cap q=\left\{\left[7;7\right]\right\} \)
1003061305
Level:
A
Determine the relative position of the lines \( p\colon 4x+6y-5=0 \) and \( q\colon y=-\frac23 x-6 \).
parallel different lines, \( p\parallel q;\ p\neq q \)
identical lines, \( p=q \)
intersecting lines, \( p\cap q=\left\{\left[0;\frac54\right]\right\} \)
intersecting lines, \( p\cap q=\left\{\left[0;\frac56\right]\right\} \)
1003061304
Level:
A
Determine the relative position of the lines
\( p\colon4x-3y+9=0 \) and
\[ \begin{aligned} q\colon x&=6+3t, \\
y&=11+4t, \end{aligned} \]
where \( t\in\mathbb{R}\).
identical lines, \( p=q \)
parallel different lines, \( p\parallel q;\ p\neq q \)
intersecting lines, \( p\cap q=\{[0;3]\} \)
intersecting lines, \( p\cap q=\{[6;11]\} \)
1103061303
Level:
A
Let there be a straight line \( p\colon 5x-y-10=0 \). Choose the equation of a straight line \( q \) that passes through the point \( A=[-2;2] \) and intersects with \( p \) on \( y \)-axis.
\( q\colon y=-6x-10 \)
\( q\colon y=-5x-10 \)
\( q\colon y=-5x-8 \)
\( q\colon y=-6x-8 \)
1103061302
Level:
A
Let there be straight lines \( p\colon x+4y-16=0 \) and \( q\colon y= \frac18 x+b \), where \( b \) is a real parameter. Specify the value of \( b \), such that \( p \) and \( q \) do intersect on \( x \)-axis.
\( b=-2 \)
\( b=-4 \)
\( b=2 \)
\( b=0 \)
1003047504
Level:
A
Find the following limit. \[ \lim\limits_{n\rightarrow\infty}\frac{3\pi}{6n^2-1} \]
\( 0 \)
\( \infty \)
\( 3\pi \)
\( \frac12 \)
\( \frac16 \)