Power and radical functions

1103143503

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^4 \) and \( g(x)=x^6 \). Identify which of the following statements is true.
The solution set of the inequality \( x^4 \leq x^6 \) is \( (-\infty; -1]\cup[1;\infty)\cup\{0\} \).
The solution set of the inequality \( x^4 > x^6 \) is \( (-1;1) \).
The solution set of the equation \( x^6=x^4 \) is \( \{0;1\} \).
The solution set of the inequality \( x^6 \geq x^4 \) is \( (-\infty; -1]\cup[1; \infty) \).

1103156802

Level: 
A
The graphs represent functions \( f(x)=x^3 \), \( x\in[0;1]\); \( g(x)=2x^3 \), \( x\in[0;1] \) and \( h(x)=x^4 \), \( x\in[0;1] \). Choose the legend which assigns the correct color of the graph to each of the given functions.
\( f \) -- red, \( g \) -- green, \( h \) -- blue
\( f \) -- blue, \( g \) -- green, \( h \) -- red
\( f \) -- blue, \( g \) -- red, \( h \) -- green
\( f \) -- green, \( g \) -- red, \( h \) -- blue

1103156803

Level: 
A
The graphs represent the functions \( f(x)=x^2 \), \( x\in[-2;0] \); \( g(x)=x^3\), \(x\in[-2;0] \) and \( h(x)=(-x)^3 \), \( x\in[-2;0] \). Choose the legend which assigns the correct color of the graph to each of the given functions.
\( f \) -- blue, \( g \) -- red, \( h \) -- green
\( f \) -- red, \( g \) -- blue, \( h \) -- green
\( f \) -- green, \( g \) -- red, \( h \) -- blue
\( f \) -- blue, \( g \) -- green, \( h \) -- red

1103159301

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

1103159302

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 true.
\( \left(\frac12\right)^{-3} < \left( \frac12 \right)^{-4} \)
\( 2^{-4} > 2^{-3} \)
\( (-2)^{-4} \leq (-2)^{-3} \)
\( (-1)^{-4} > 1^{-3} \)

1103159303

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-3} \). Identify which of the following statements is true.
\( -\left(\frac12\right)^{-3} < (-2)^{-3} \)
\( (-2)^{-2} \leq -2^{-2} \)
\( (-2)^{-3} < -2^{-3} \)
\( (-2)^{-3} \leq -2^{-2} \)

1103161001

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-3} \). Identify which of the following statements is false.
The solution set of the inequality \( x^{-2} > 0 \) is \( (-\infty;\infty) \).
The solution set of the inequality \( x^{-3} > 0 \) is \( (0;\infty) \).
The solution set of the equation \( x^{-3} = x^{-2} \) is \( \{1\} \).
The solution set of the inequality \( x^{-3} < x^{-2} \) is \( (-\infty;0)\cup(1;\infty) \).

1103161002

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-4} \). Identify which of the following inequalities has the solution set \( (-\infty; -1]\cup[1;\infty) \).
\( x^{-4} \leq x^{-2} \)
\( x^{-2} \leq x^{-4} \)
\( x^{-2} > x^{-4} \)
\( x^{-2} < 1 \)

1103161003

Level: 
A
The graphs represent the parts of the functions \( f(x)=x^{-2} \) and \( g(x)=x^{-3} \). Identify which of the following inequalities has the solution set \( (-\infty;-1)\cup(0;\infty) \).
\( -x^{-3} < x^{-2} \)
\( \left|x^{-3}\right| < x^{-2} \)
\( x^{-3} < -x^{-2} \)
\( x^{-3} < \left|x^{-2}\right| \)