1003030804
Level:
B
Identify which of the following functions is decreasing in the interval \( [ 0,\infty ) \).
\( m(x)=-x^2 \)
\( h(x) = \frac1x \)
\( g(x) = -100+0.1x \)
\( f(x) = (-x)^2 \)
Properties of Functions
1003030805
Level:
B
Identify which of the following functions is increasing in the interval \( [ 1,\infty ) \).
\( m(x)=(1-x)^2 \)
\( g(x)=1-x \)
\( h(x)=1-x^2 \)
\( f(x)=1-x^3 \)
1003030807
Level:
B
The function \( f(x) \) is increasing in the interval \( J \). Identify which of the following statements is false.
The function \( h(x) = -2 f(x) \) is increasing in the interval \( J \).
The function \( g(x) = 2 f(x) \) is increasing in the interval \( J \).
The function \( m(x) = f(x)+2 \) is increasing in the interval \( J \).
The function \( n(x) = f(x)-2 \) is increasing in the interval \( J \).
1003030904
Level:
B
Identify which of the following functions is not bounded above.
\( m(x)=3-x^3 \)
\( h(x)=3 \)
\( g(x)=3-x^2 \)
\( f(x)= 3-\sqrt x \)
1003048504
Level:
B
Identify which of the following functions is not periodic.
\( m(x)=(-2)^x,x\in\mathbb{Z} \)
\( h(x)=(-1)^x,x\in\mathbb{Z} \)
\( g(x)=-2,x\in\mathbb{R} \)
\( f(x)= 1^x,x\in\mathbb{R} \)
1003048505
Level:
B
Every real number \( x \) can be written as \( x=c+d \), where \( c \) is an integer and \( d\in[0, 1) \). Then \( c \) is called the integer part of \( x \) and is denoted by \( [x] \). Which of the following functions has the biggest primitive period?
\( g(x)=(-1)^{[x]} \)
\( f(x)=[2x]-2x \)
\( m(x)=3[x]-3x \)
\( h(x)=[x]-x \)
1003048507
Level:
B
Let \( f \) be any periodic function. Identify which of the following statements is true.
The function \( f \) is not an injective (one-to-one) function.
\( D(f)=\mathbb{R} \).
The function \( f \) is bounded.
The function \( f \) is increasing.
2000002401
Level:
B
Find the domain of the function \( f(x) = \sqrt{ \frac{1-x}{x+1}}\).
\( ( -1 , 1 ] \)
\( ( -1 , 1 ) \)
\( \mathbb{R} \setminus \{ -1,1\} \)
\( ( -\infty , 1) \cup [ 1, \infty) \)
2000002402
Level:
B
Find the domain of the function \( f(x)= \frac{x^2 -1}{(x+1)^2}\).
\( \mathbb{R} \setminus \{-1\} \)
\( (-1,\infty ) \)
\( (-\infty, -1) \cup (1,\infty) \)
\( [ -1, \infty) \)
2000002403
Level:
B
Find the domain of the function \( f(x)=\frac{1}{|x-3|}\).
\( \mathbb{R} \setminus \{3\} \)
\( \mathbb{R} \)
\( (3,\infty) \)
\( (-3,3) \)