Power and Radical Functions

1103143501

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^3 \) and \( g(x)=x^4 \). Identify which of the following statements is false.
The solution set of the inequality \( x^4 > x^3 \) is \( (1,\infty) \).
The solution set of the inequality \( x^4 > 0 \) is \( (-\infty,0)\cup(0,\infty) \).
The solution set of the equation \( x^3 = x^4 \) is \( \{0,1\} \).
The solution set of the inequality \( x^3 \geq x^4 \) is \( [0,1] \).

1103143403

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^3 ,\ g(x)=x^4,\ h(x)=x^5 \). Identify which of the following statements is false.
\( \left(-\frac13\right)^5 < \left(-\frac13\right)^3 \)
\( \left(\frac12\right)^5 < \left(-\frac12\right)^4 \)
\( (-3)^4 > (3)^3 \)
\( \left(\frac14\right)^3 \geq (-0.25)^4 \)

1103143401

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^3 \) and \( g(x)=x^4 \). Identify which of the following statements is false.
\( \left(-\frac12\right)^3 > (2)^3 \)
\( (-2)^3 < \left(-\frac12\right)^3 \)
\( \left(\frac13\right)^3 \geq (0.3)^3 \)
\( (-1)^3 \leq (1)^3 \)

9000025801

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

9000025804

Level: 
B
In the following list identify a true statement on the function \(f\). \[ f(x) = (x + 1)(x + 2)(x - 3) \]
The function \(f\) is positive on \(I_{1} = (-2,-1)\) and \(I_{2} = (3,\infty )\).
The function \(f\) is an increasing function (in its whole domain).
The function is decreasing only on \(I = (-1,3)\).
The function is decreasing on \(I_{1} = (-\infty ,-2)\) and \(I_{2} = (3,\infty )\).