1003123901
Level:
B
Given \( f(x)=\frac{2x+3}{x-5} \), find the true statement in the following list.
\( f(x)=2+\frac{13}{x-5} \)
\( f(x)=2+\frac3{x-5} \)
\( f(x)=2x+\frac3{x-5} \)
\( f(x)=3+\frac{2x}{x-5} \)
Rational functions
1103124602
Level:
C
Let \( f(x)=\frac{x^2-x-6}{x^2-9} \). One of the following pictures shows a part of the graph of \( f \). Choose the picture.
1003124601
Level:
B
Let \( f(x)=\frac{2x}{x^2-1} \). Find the true statement.
\( \forall x\in(-\infty;-1)\cup(0;1)\colon f(x) < 0 \).
The domain of \( f \) is \( (-\infty;1)\cup(1;\infty) \).
\( \forall x\in(-1;1)\colon f(x) \leq 0 \).
The domain of \( f \) is \( (-\infty;-1)\cup(-1;0)\cup(0;1)\cup(1;\infty) \).
1003118307
Level:
C
Identify which of the following functions has the maximum at \( x=-\frac12 \).
\( m(x)=-\left|\frac{4x+2}{x-2}\right| \)
\( g(x)=\left|-\frac{5x+10}{2x-1}\right| \)
\( f(x)=-\left|\frac{2x+1}{4x+2}\right| \)
\( h(x)=-\left|\frac{x+1}{2x-2}\right| \)
1003118306
Level:
C
Find the true statement about the function \( f(x)=\left|\frac{4x-4}{2x-1}\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac12\right)\cup\left(\frac12;\infty\right) \).
The range of the function \( f \) is the set \( [0;2)\cup(2;\infty) \).
The function \( f \) has the minimum at \( x=4 \).
The function \( f \) is an injective (one-to-one) function.
1003118305
Level:
C
Find the false statement about the function \( f(x)=\left|\frac1{2-3x}-3\right| \).
The domain of the function \( f \) is the set \( \left(-\infty;\frac32\right)\cup\left(\frac32;\infty\right) \).
The range of the function \( f \) is the interval \( \left[0;\infty\right) \).
The function \( f \) has the minimum at \( x=\frac59 \).
The function \( f \) is bounded below.
1003118304
Level:
C
Identify which of the following functions is bounded.
\( h(x)=\frac{3x-6}{2x-4} \)
\( f(x)=\frac{3x-6}{2x} \)
\( g(x)=3-\frac6{2x} \)
\( m(x)=\left|\frac{4x-3}{2x-6}\right| \)
1003118303
Level:
B
Find the false statement about the function \( f(x)=\frac{4x+1}{3-2x};\ x\in[2;\infty) \).
The function \( f \) has no minimum.
The function \( f \) is increasing.
The function \( f \) has no maximum.
The function \( f \) is bounded.
1003118302
Level:
B
Find the true statement about the function \( f(x)=1-\frac2{0.5x-1};\ x\in[-3;1)\cup(2;6] \).
The function \( f \) has no maximum.
The function \( f \) has the maximum at \( x=6 \).
The function \( f \) has the minimum at \( x=-3 \).
The function \( f \) is bounded.
1003118301
Level:
B
Find the true statement about the function \( f(x)=-1+\frac3{2x-6} \).
The function \( f \) is decreasing on the interval \( (3;\infty) \).
The function \( f \) is decreasing on the interval \( (-3;\infty) \).
The function \( f \) is decreasing on the interval \( (-\infty;6) \).
The function \( f \) is decreasing on the interval \( (-1;\infty) \).