Properties of Functions

1103025601

Level: 
A
The function \( f \) is given by the graph. Which of the following statements is true?
The function \( f \) has a minimum and a maximum at every \( x \) of its domain.
The function \( f \) has the minimum at \( x=-6 \) and the maximum at \( x=3 \).
The function \( f \) has the maximum at \( x=3 \) and it has no minimum.
The function \( f \) has neither a minimum nor a maximum.

1103028409

Level: 
A
The function \( f \) is given by the graph. Which of the statements about the domain and the range of the function \( f \) is true?
\( D(f) =[-3,4], H(f)=[-2,2)\cup(2, 3]\cup\{5\} \)
\( D(f) =[-3,1)\cup(1, 4], H(f)=[-2, 2)\cup(2, 3] \)
\( D(f)=[-3,4], H(f)=[-2,5] \)
\( D(f) =[-3,4], H(f)=[-2,3]\cup\{5\} \)

1103030802

Level: 
A
The function \( f \) is given by the graph. Identify which of the following statements is true.
The function \( f \) is neither increasing nor decreasing.
The function \( f \) is increasing.
The function \( f \) is non-decreasing.
The function \( f \) is increasing in the interval \( [ -4,1] \).

1103030803

Level: 
A
There is a part of the graph of the function \( f(x)=x^3 \) in the picture. Identify which of the following statements is true.
The function \( f \) is increasing in the interval \( [ -1,1 ] \).
The function \( f \) is decreasing in the interval \( [ -1,1 ] \).
The function \( f \) is non-decreasing and it is not increasing in the interval \( [ -1,1 ] \).
The function \( f \) is non-increasing in the interval \( [ -1,1 ] \).

1103030806

Level: 
A
The function \( f \) is given by the graph. Identify which of the following statements is false.
The function \( f \) is non-increasing in the interval \( [ -3,2 ] \).
The function \( f \) is not increasing.
The function \( f \) is decreasing in the interval \( [ 2,5 ] \).
The function \( f \) is non-decreasing in the interval \( [ -1,2 ] \).