Linear Functions with Absolute Values

1103072504

Level:

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

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

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

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

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

1103072503

Level:

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

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

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

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

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

1103072502

Level:

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

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

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

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

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

1103072501

Level:

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

\( f(x)=x-|x|,\ x\in[-4,4] \)

\( f(x)=x+|x|,\ x\in[-4,4] \)

\( f(x)=|x|-x,\ x\in[-4,4] \)

\( f(x)=-x-|x|,\ x\in[-4,4] \)

1003019303

Level:

Let \( f(x)=|2-x|+|x+1| \). Identify which of the statements is correct.

Function \( f \) has minimum at \( x=-1 \) and at \( x=2 \).

Function \( f \) has minimum at \( x=-1 \) and maximum at \( x=2 \).

Function \( f \) has maximum at \( x=-1 \) and at \( x=2 \).

Function \( f \) has minimum at \( x=3 \).

1003019302

Level:

Which of the following functions has minimum at \( x=3 \)?

\( f(x)=2|x-3|+1 \)

\( h(x)=2|x+3|-1 \)

\( g(x)=-2|x-3|+3 \)

\( m(x)=2|x+3| \)

9000024504

Level:

Identify the value of a real parameter \(b\) such that the graph of the function \[ f(x) = |x - 0.5| + b \] corresponds to the picture.

\(1\)

\(- 1\)

\(- 0.5\)

\(0.5\)

\(1.5\)

9000024505

Level:

Identify the value of a real parameter \(b\) such that the graph of the function \[ f(x) = \left |x + \frac{1} {2}\right | + b \] corresponds to the picture.

\(- 1\)

\(-\frac{3} {2}\)

\(-\frac{1} {2}\)

\(\frac{1} {2}\)

\(1\)

9000024506

Level:

Identify the value of real parameters \(a\) and \(b\) such that the graph of the function \[ f(x)= \left |x + a\right | + b \] corresponds to the picture.

\(a = 2,\ b = -3\)

\(a = 2,\ b = 3\)

\(a = 3,\ b = 2\)

\(a = -3,\ b = -2\)

9000024507

Level:

Identify the value of a real parameter \(a\) such that the graph of the function \[ f(x) = -|a - x| + 2 \] corresponds to the picture.

\(3\)

\(2\)

\(1\)

\(- 1\)

\(4\)

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Linear Functions with Absolute Values

1103072504

1103072503

1103072502

1103072501

1003019303

1003019302

9000024504

9000024505

9000024506

9000024507

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