Graphs of Linear Functions\\ with Absolute Values
Linear functions with absolute values
1103162909
Level:
B
With aid of the graph of a function \( f \) find all \( x\), so that \( |f(x)|=3 \).
\( x\in\{-5;1\} \)
\(x\in \{1\} \)
\(x\in \{-2\} \)
\( x\in\{-5;5\} \)
1103162908
Level:
B
With aid of the given graph of a function \( f \), find all \( x \) so that \( |f(x)-2|=1 \).
\( x\in\{-4;-2\} \)
\( x\in\{-4;2\} \)
\( x\in\{-2;2\} \)
\( x\in\{-3\} \)
1003187206
Level:
C
How many \( x \)-intercepts does the graph of \( f(x)=\left|-|2-x|- 2\right| \) have?
\( 0 \)
\( 2 \)
\( 1 \)
\( 4 \)
1003187205
Level:
C
Let \( f(x)=\left|3|2x-1|-9\right| \). The number of argument values \( x \) for which \( f(x)=2 \) is:
\( 4 \)
\( 2 \)
\( 3 \)
\( 1 \)
1003030905
Level:
B
Let \( f(x)=|x-1|-2|x| \). Identify which of the following statements is true.
The function \( f \) is bounded above and is not bounded below.
The function \( f \) is bounded below and is not bounded above.
The function \( f \) is bounded.
The function \( f \) is neither bounded above nor bounded below.
1003102303
Level:
C
Which of the following functions is decreasing on the interval \( (-\infty;0) \)?
\( m(x)=\left|x-|x-1|\right| \)
\( h(x)=\left| x+|x-1|\right| \)
\( g(x)=\left|x-|x+1|\right| \)
\( f(x)=\left|x+|x+1|\right| \)
1003102302
Level:
C
Let \( f(x)=|1-|x| | \). Which of the following statements is true?
Function \( f \) has minimum at \( x=-1 \).
Function \( f \) is bounded.
Function \( f \) is increasing on the interval \( (0;\infty) \).
The range of \( f \) is \( [1;\infty) \).
1103102301
Level:
C
Let \( f(x)=|x-|x| | \), \( x\in [-5;5] \). Choose the graph of \( f \).
1003049306
Level:
B
Identify which of the following functions is odd.
\( g(x)=|x|-|-x| \)
\( h(x)=|x|-x \)
\( f(x)=-|-x| \)
\( m(x)=|-1| \)