1003199905
Level:
B
Let \( f(x)=\left(\frac{x^2}{\sqrt[3]x}\right)^{-0.5} \). Identify which of the following statements is true.
\( f(x)=x^{-\frac56} \)
\( f(x)=x^{\frac13} \)
\( f(x)=x^{-\frac16} \)
\( f(x)=x^{\frac76} \)
Power and radical functions
1003199904
Level:
B
Let \( f(x)=x^{\frac12} \) and \( g(x)=x^{\frac32} \). Identify which of the following statements is true.
\( \frac{f(2)}{g(2)} =0.5 \)
\( f(2)+g(2)=4 \)
\( f(4)\cdot g(4)=8 \)
\( \bigl(f(2)\bigr)^{\frac32}=4 \)
1003199903
Level:
B
Let \( f(x)=x^{-\frac32} \). Identify which of the following statements is false.
\( f(8)=0.25 \)
\( f(100)=0.001 \)
\( f(\frac1{16})=64 \)
\( f(\frac12)=2\sqrt2 \)
1003199902
Level:
B
Let \( f(x)=x^{\frac23} \). Identify which of the following statements is true.
\( f(27)=9 \)
\( f(16)=64 \)
\( f(\frac18)=4 \)
\( f(0.0125)=0.25 \)
1003199901
Level:
B
Let \( f(x)=x^{\frac12} \). Identify which of the following statements is false.
\( f(0.25)=16 \)
\( f(0.0121)=0.11 \)
\( f(\frac12)=\frac{\sqrt2}2 \)
\( f(338)=13\sqrt2 \)
1103186201
Level:
B
Identify which of the graphs represents a part of the function \( f(x)=\sqrt{-x} \).
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
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
1103156801
Level:
A
Function \( f \) is given by the graph. Identify the equation of the function \( f \).
\( f(x)=8-(x-1)^3;\ x\in[0;3] \)
\( f(x)=9-x^5;\ x\in[0;3] \)
\( f(x)=\left|(x+1)^2+8\right|;\ x\in[0;3] \)
\( f(x)=(x+1)^3+8;\ x\in[0;3] \)
1003164105
Level:
B
Let \( f(x)=\sqrt{x^2} \) and \( g(x)=x \). Identify which of the following statements is true.
\( f(-3)=3 \)
\( f(-5)=-5 \)
\(\forall x \in \mathbb{R}: f(x)=g(x) \)
\(\forall x \in \mathbb{R}: f(x)=-g(x) \)