Power and radical functions
Graph of the function $f(x)=a\pm\sqrt[3]{bx+c}$, where $a$, $b$, $c\in\mathbb{R}$
Submitted by vladimir.arzt on Fri, 08/30/2024 - 10:18Graph of the function $f(x)=\pm\sqrt[n]{\pm x}$, where $n\in\mathbb{N}$
Submitted by vladimir.arzt on Fri, 08/30/2024 - 09:19Domain and Range of Power Functions with Absolute Value
Submitted by vladimir.arzt on Sun, 08/25/2024 - 18:052110014806
Level:
C
Identify the graph of the function \( f(x)=-\sqrt{|x|};\ x\in [ -9;9] \).
2010014805
Level:
C
Choose the function that describes the dependence of a cube surface \( S \) on the length of its space diagonal \( u \).
\( S=2u^2;\ u\in(0;\infty) \)
\( S=6u^2;\ u\in(0;\infty) \)
\( S=3u^2;\ u\in(0;\infty) \)
\( S=18u^2;\ u\in(0;\infty) \)
2010014804
Level:
C
Find the true statement about the function \( f(x)=\left|x^4-1\right| \).
The function \( f \) has the minima at \( x=-1 \) and \( x=1 \).
The function \( f \) has no minimum.
The function \( f \) has the minimum at \( x=0 \).
The function \( f \) has the minima at \( x=-1 \), \(x=0\) and \( x=1 \).
2110014803
Level:
B
Identify which of the graphs represents a part of the function \( f(x)=-\sqrt{x} \).
2010014802
Level:
B
In the following list identify a function with a domain
\(\left (\frac13;\infty \right)\).
\(f(x)= \sqrt{ \frac{5}
{9x-3}}\)
\(f(x)= \sqrt{ \frac{9x-3}
{5}}\)
\(f(x)= \sqrt{9x-3}\)
\(f(x)= \sqrt{ \frac{9x-3}
{3x}}\)
2010014801
Level:
B
Let \( f(x)=\sqrt[3]{(-x)^3} \) and \( g(x)=-x \). Identify which of the following statements is true.
\( f(x)=g(x) \)
\( f(-2)=-8 \)
\( g(-2)=-2 \)
\( f(x)=-g(x) \)