2010009203
Level:
B
Function \( f \) is given by the graph. Identify which of the following statements is true.
\( f(x)=2|x|+x;\ x\in [ -3;2 ] \)
\( f(x)=2|x|-x;\ x\in [ -3;2 ] \)
\( f(x)=-x-2|x|;\ x\in [ -3;2 ] \)
\( f(x)=x-2|x|;\ x\in [ -3;2 ] \)
Functions with absolute values
2010009204
Level:
B
Function \( f \) is given by the graph. Identify which of the following statements is true.
\( f(x)=|x-1|-|x|;\ x\in [ -4;2 ] \)
\( f(x)=|x+1|-|x|;\ x\in [ -4;2 ] \)
\( f(x)=|x+1|+|x|;\ x\in [ -4;2 ] \)
\( f(x)=|x|-|x-1|;\ x\in [ -4;2 ] \)
1003049202
Level:
C
Let \( f(x)=|x|-|3-2|x| | \). Identify which of the following function values is the smallest.
\( f(-6.5) \)
\( f(-2) \)
\( f(0) \)
\( f(0.5) \)
1003049204
Level:
C
Let \( f(x)=|x| \). Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon f(a+b)=f(a)+f(b) \)
\( \forall a\text{, }b\in\mathbb{R}\colon f(a\cdot b)=f(a)\cdot f(b) \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon f(\frac ab)=\frac{f(a)}{f(b)} \)
\( \forall a\in\mathbb{R}\colon f(a)=f(-a) \)
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 \( [1;\infty) \).
1003102303
Level:
C
Which of the following functions is decreasing on the interval \( (-\infty;0) \)?
\( m(x)=\left|x-|x-1|\right| \)
\( h(x)=\left| x+|x-1|\right| \)
\( g(x)=\left|x-|x+1|\right| \)
\( f(x)=\left|x+|x+1|\right| \)
1003187205
Level:
C
Let \( f(x)=\left|3|2x-1|-9\right| \). The number of argument values \( x \) for which \( f(x)=2 \) is:
\( 4 \)
\( 2 \)
\( 3 \)
\( 1 \)
1003187206
Level:
C
How many \( x \)-intercepts does the graph of \( f(x)=\left|-|2-x|- 2\right| \) have?
\( 0 \)
\( 2 \)
\( 1 \)
\( 4 \)
1103102301
Level:
C
Let \( f(x)=|x-|x| | \), \( x\in [-5;5] \). Choose the graph of \( f \).
2000018601
Level:
C
Which of the following functions is increasing on the interval \([ -1;\infty)\)?
\( f(x)= 2\bigl| |x+3|-2\bigr|\)
\( g(x)= 2\bigl| |x-3|-2\bigr|\)
\( h(x)= -2\bigl| |x+3|-2\bigr|\)
\( k(x)= 2\bigl| |x-3|+2\bigr|\)