Rational functions

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.

1103102304

Level: 
C
Function \( f \) is given completely by the graph. Which of the following statements is false?
\( f(x)=\frac{|x|}x,\ x\in[-5;0)\cup(0;5] \)
\( f(x)=\left|\frac{|x|}x\right|,\ x\in[-5;0)\cup(0;5] \)
\( f(x)=1,\ x\in[-5;0)\cup(0;5] \)
\( f(x)=\frac{x}x,\ x\in[-5;0)\cup(0;5] \)

2010009904

Level: 
C
A part of the graph of the function \( f(x)=\frac{-3}x \) is shown in the picture. Identify which of the following statements is true.
The function \( g \) defined by \( g(x)=-\left|f(x)\right| \) is bounded above.
The function \( m \) defined by \( m(x)=\left|f(x)\right| \) is bounded above.
The function \( h \) defined by \( h(x)=-f(x)\) is bounded below.
The function \( f \) is bounded below.

2010017302

Level: 
C
Find the interval where the function \(f(x) = -\left |2+\frac{1} {x}\right |\) is a decreasing function. The function \(f\) is graphed in the picture.
\(\left[ -\frac12; 0\right)\)
\((-\infty ;0)\)
\(\left[ -\frac12; \infty\right)\)
\(\left(-\infty ; -\frac12\right)\)

2010017304

Level: 
C
Consider the functions \[ \text{$f(x)= -\frac{2} {3x}$ and $g(x) = \frac{k} {x}$.} \] Identify the value of the coefficient \(k\) which ensures that the graphs of both functions are symmetric about \(y\)-axis.
\( k=\frac23\)
\( k=\frac32\)
\( k=-\frac23\)
\( k=-\frac32\)