1003049306 Level: BIdentify which of the following functions is odd.\( g(x)=|x|-|-x| \)\( h(x)=|x|-x \)\( f(x)=-|-x| \)\( m(x)=|-1| \)
1003049305 Level: BIdentify a real number \( a \) such that the function \( f(x)=a|-12-ax|-a \) has a maximum at \( x=3 \).\( -4 \)\( 3 \)\( 4 \)There is no such number.
1003049304 Level: BIdentify which of the following functions is increasing in the interval \( (-\infty; +2] \).\( m(x)=-2|5-x|+1 \)\( h(x)=|x|+2 \)\( g(x)=-|x|-2 \)\( f(x)=-|x+2| \)
1003049303 Level: BLet \( f(x)=-|x+3| \). 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 \( (-\infty; 0] \).
1003049302 Level: BLet \( f(x)=2|-x|+1 \). 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 \( (-\infty; 0] \).
1003049301 Level: BLet \( f(x)=\frac12 (|x|-3) \). 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.
1003072705 Level: BFind the false statement about the function \( f(x)=|x+1|-|x-2|+|x| \).The function \( f \) is injective (one-to-one).The function \( f \) has minimum at \( x=-1 \).The function \( f \) is bounded below.The range of the function \( f \) is \( [-2;\infty) \).
1003072704 Level: BFind the true statement about the function \( f(x)=2|x-2|-|x-1|-x \).The function \( f \) has minimum at \( x=3 \).The function \( f \) has maximum at \( x=1 \).The function \( f \) has minimum at \( x=-3 \).The function \( f \) has no minimum.
1003072703 Level: BFind the true statement about the domain or the range of the function \( f(x)=|x+2|-|1-x| \).\( H(f)=[-3;3] \)\( D(f)=[-3;3] \)\( H(f)=\mathbb{R} \)\( D(f)=[-2;1] \)
1003072702 Level: BWhich of the following functions is bounded?\( g(x)=|x-2|-|x| \)\( f(x)=|x-2|+|x| \)\( h(x)=|x+2|+|x| \)\( m(x)=|2x|-|x| \)