A

9000025805

Level: 
A
In the following list identify a true statement on the function \(f\). \[ f(x) = (x + 1)(x + 2)(x - 3) \]
\(f(x) < 0 \iff x\in (-\infty ;-2)\cup (-1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3} {2}\right )\cup (1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3} {2}\right )\cup (3;\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3} {2};-1\right )\cup (3;\infty )\)

9000024108

Level: 
A
Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ \frac{x + 1} {2} -\frac{x - 2} {3} = \frac{x} {4} \]
multiply by \(12\)
multiply by \(2\)
multiply by \(3\)
multiply by \(4\)
multiply by \(24\)
multiply by \((2x + 1)(x - 2)x\), assuming \(x\not \in \left \{-\frac{1} {2};2;0\right \}\)

9000024110

Level: 
A
Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ 11x - 2 = 2 - 4x \]
add \((4x + 2)\)
multiply by \(\frac{1} {11}\)
multiply by \(\left (-\frac{1} {4}\right )\)
add \((-11x + 4x)\)
subtract \((4x + 2)\)
add \((4x + 2)\)

9000025801

Level: 
A
Find all intersections of the graph of the following function with \(x\)-axis. \[ f(x) = x^{3} - x^{2} - 2x \]
\(X_{1} = [0;0]\), \(X_{2} = [-1;0]\), \(X_{3} = [2;0]\)
\(X = [0;0]\)
\(X_{1} = [0;0]\), \(X_{2} = [-1;0]\)
\(X_{1} = [0;0]\), \(X_{2} = [1;0]\), \(X_{3} = [-2;0]\)