1003199902
Level:
B
Let \( f(x)=x^{\frac23} \). Identify which of the following statements is true.
\( f(27)=9 \)
\( f(16)=64 \)
\( f(\frac18)=4 \)
\( f(0.0125)=0.25 \)
Power and radical functions
1003199903
Level:
B
Let \( f(x)=x^{-\frac32} \). Identify which of the following statements is false.
\( f(8)=0.25 \)
\( f(100)=0.001 \)
\( f(\frac1{16})=64 \)
\( f(\frac12)=2\sqrt2 \)
1003199904
Level:
B
Let \( f(x)=x^{\frac12} \) and \( g(x)=x^{\frac32} \). Identify which of the following statements is true.
\( \frac{f(2)}{g(2)} =0.5 \)
\( f(2)+g(2)=4 \)
\( f(4)\cdot g(4)=8 \)
\( \bigl(f(2)\bigr)^{\frac32}=4 \)
1003199905
Level:
B
Let \( f(x)=\left(\frac{x^2}{\sqrt[3]x}\right)^{-0.5} \). Identify which of the following statements is true.
\( f(x)=x^{-\frac56} \)
\( f(x)=x^{\frac13} \)
\( f(x)=x^{-\frac16} \)
\( f(x)=x^{\frac76} \)
1103186201
Level:
B
Identify which of the graphs represents a part of the function \( f(x)=\sqrt{-x} \).
2000001703
Level:
B
The graphs represent the parts of the functions \(f(x)= \sqrt{x}\), \(g(x)=\sqrt[4]{x}\) and \(h(x)=\sqrt[10]{x}\). 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
\(f\) — green, \(g\) — red, \(h\) — blue
\(f\) — green, \(g\) — blue, \(h\) — red
2000001704
Level:
B
The graphs represent the parts of the functions \(f(x)= \sqrt[3]{x}\), \(g(x)=\sqrt[5]{x}\) and \(h(x)=\sqrt[9]{x}\). 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
\(f\) — green, \(g\) — red, \(h\) — blue
\(f\) — green, \(g\) — blue, \(h\) — red
2010014801
Level:
B
Let \( f(x)=\sqrt[3]{(-x)^3} \) and \( g(x)=-x \). Identify which of the following statements is true.
\( f(x)=g(x) \)
\( f(-2)=-8 \)
\( g(-2)=-2 \)
\( f(x)=-g(x) \)
2010014802
Level:
B
In the following list identify a function with a domain
\(\left (\frac13;\infty \right)\).
\(f(x)= \sqrt{ \frac{5}
{9x-3}}\)
\(f(x)= \sqrt{ \frac{9x-3}
{5}}\)
\(f(x)= \sqrt{9x-3}\)
\(f(x)= \sqrt{ \frac{9x-3}
{3x}}\)
2100001701
Level:
B
Identify which of the graphs represents a part of the function \(f(x) = \sqrt{x} \).
