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2010009204

Level:

Function \( f \) is given by the graph. Identify which of the following statements is true.

\( f(x)=|x-1|-|x|;\ x\in [ -4;2 ] \)

\( f(x)=|x+1|-|x|;\ x\in [ -4;2 ] \)

\( f(x)=|x+1|+|x|;\ x\in [ -4;2 ] \)

\( f(x)=|x|-|x-1|;\ x\in [ -4;2 ] \)

2010009203

Level:

Function \( f \) is given by the graph. Identify which of the following statements is true.

\( f(x)=2|x|+x;\ x\in [ -3;2 ] \)

\( f(x)=2|x|-x;\ x\in [ -3;2 ] \)

\( f(x)=-x-2|x|;\ x\in [ -3;2 ] \)

\( f(x)=x-2|x|;\ x\in [ -3;2 ] \)

2010009202

Level:

Which of the following functions is bounded?

\( f(x)=|3+x|-|x| \)

\( g(x)=|3+x|+|x| \)

\( h(x)=|x-3|+|x| \)

\( m(x)=3-|x| \)

2010008810

Level:

Factor the expression: \[(2 - b)(b -7) - 5(b -7)(2b - 3) - (7 -b)^2\]

\(12(b - 7)(2 - b)\)

\(12(b - 7)(b - 2)\)

\(10(b - 7)(1 - b)\)

\(10(b - 7)(b - 1)\)

2010008809

Level:

Factor the expression: \[(4 + a)(a - 3) - (3 - a)^2 - 3(a - 3)(2a + 1)\]

\(2(a - 3)(2 - 3a)\)

\(2(a - 3)(3a - 2)\)

\(2(3 - a)(2a + 1)\)

\(2(a - 3)(2a + 1)\)

2010008808

Level:

Factor the expression: \[4(3y - x)^2 - 25(y - 2x)^2\]

\((8x + y)(11y - 12x)\)

\((8x + y)(11y + 8x)\)

\((y - 12x)(11y - 12x)\)

\((y - 12x)(11y + 8x)\)

2010008807

Level:

Factor the expression: \[9(3t - 2z)^2 - 16(t - 2z)^2\]

\((5t + 2z)(13t - 14z)\)

\((5t + 2z)(3t - 4z)\)

\((5t - 14z)(13t - 14z)\)

\((5t - 14z)(3t - 4z)\)

2010008602

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval. \[|2x-3|+ 2|2-x |= 1-3x\]

\( \left(\frac32 ;\infty\right) \)

\( \left(-\infty;2\right) \)

\( \left(2 ;\infty\right) \)

\( \left(-\infty;\frac32\right) \)

2010008605

Level:

Find the sum of all the roots of the equation \( |2x+5|=|2-x| \).

\( -8\)

\( -9\)

\( -7\)

\( -1 \)

2010008603

Level:

Calculate for which values of the parameter \(t \in\mathbb{R} \) the given equation has no solution. \[ |2-4x|=1-t\]

\( t\in (1 ;\infty) \)

\( t\in (-\infty;1) \)

\( t\in \left(\frac12 ;\infty\right) \)

\( t\in \left(-\infty;\frac12\right) \)

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