Functions with absolute values

1003019303

Level: 
B
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 \( x=3 \).

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.

1003049301

Level: 
B
Let \( f(x)=\frac12 (|x|-3) \). Identify which of the following statements is false.
The range of the function \( f \) is the interval \( [-3;\infty ) \).
The domain of the function \( f \) is the interval \( (-\infty;\infty) \).
The function \( f \) is even.
The function \( f \) is bounded below.

1003049302

Level: 
B
Let \( f(x)=2|-x|+1 \). Identify which of the following statements is false.
The function \( f \) is an injective (one-to-one) function.
The function \( f \) is increasing in the interval \( [0; \infty) \).
The function \( f \) has minimum at \( x=0 \).
The function \( f \) is non-increasing in the interval \( (-\infty; 0] \).

1003049303

Level: 
B
Let \( f(x)=-|x+3| \). Identify which of the following statements is false.
The function \( f \) is even.
The function \( f \) is decreasing in the interval \( [3; \infty) \).
The function \( f \) has maximum at \( x=-3 \).
The range of the function \( f \) is the interval \( (-\infty; 0] \).