1003072702
Level:
B
Which of the following functions is bounded?
\( g(x)=|x-2|-|x| \)
\( f(x)=|x-2|+|x| \)
\( h(x)=|x+2|+|x| \)
\( m(x)=|2x|-|x| \)
Linear Functions with Absolute Values
1003072703
Level:
B
Find the true statement about the domain or the range of the function \( f(x)=|x+2|-|1-x| \).
\( H(f)=[-3,3] \)
\( D(f)=[-3,3] \)
\( H(f)=\mathbb{R} \)
\( D(f)=[-2,1] \)
1003072704
Level:
B
Find the true statement about the function \( f(x)=2|x-2|-|x-1|-x \).
The function \( f \) has minimum at \( x=3 \).
The function \( f \) has maximum at \( x=1 \).
The function \( f \) has minimum at \( x=-3 \).
The function \( f \) has no minimum.
1003072705
Level:
B
Find the false statement about the function \( f(x)=|x+1|-|x-2|+|x| \).
The function \( f \) is injective (one-to-one).
The function \( f \) has minimum at \( x=-1 \).
The function \( f \) is bounded below.
The range of the function \( f \) is \( [-2,\infty) \).
1103072501
Level:
B
Function \( f \) is given by the graph. Identify which of the following statements is true.
\( f(x)=x-|x|,\ x\in[-4,4] \)
\( f(x)=x+|x|,\ x\in[-4,4] \)
\( f(x)=|x|-x,\ x\in[-4,4] \)
\( f(x)=-x-|x|,\ x\in[-4,4] \)
1103072502
Level:
B
Function \( f \) is given by the graph. Identify which of the following statements is true.
\( f(x)=|x+1|-x,\ x\in[-4,4] \)
\( f(x)=|x|-x+1,\ x\in[-4,4] \)
\( f(x)=x-|x+1|,\ x\in[-4,4] \)
\( f(x)=x-|x|+1,\ x\in[-4,4] \)
1103072503
Level:
B
Function \( f \) is given by the graph. Identify which of the following statements is true.
\( f(x)=|x|-|x-2|,\ x\in[-4,4] \)
\( f(x)=|x|-|x+2|,\ x\in[-4,4] \)
\( f(x)=|x+2|-|x|,\ x\in[-4,4] \)
\( f(x)=|x-2|-|x|,\ x\in[-4,4] \)
1103072504
Level:
B
Function \( f \) is given by the graph. Identify which of the following statements is false.
\( f(x)=|x-1|-|2x|,\ x\in[-4,4] \)
\( f(x)=|2x|-|x-1|,\ x\in[-4,4] \)
\( f(x)=|2x|-|1-x|,\ x\in[-4,4] \)
\( f(x)=2|x|-|x-1|,\ x\in[-4,4] \)
1103072505
Level:
B
Identify which of the graphs represents the function \( f(x)=|2x-4|-|x-1|,\ x\in [-4,4] \).
1103072506
Level:
B
Identify which of the graphs below represents the function \( f(x)=x+1-|x+1|,\ x\in [-4;4] \).
