2000002403
Level:
B
Find the domain of the function \( f(x)=\frac{1}{|x-3|}\).
\( \mathbb{R} \setminus \{3\} \)
\( \mathbb{R} \)
\( (3;\infty) \)
\( (-3;3) \)
Properties of functions
2000002404
Level:
B
Decide which of the functions is even.
\( f(x) = -x^2 +3 \)
\( f(x) = \frac{x}{x^2} \)
\( f(x)=-2x^3 \)
\( f(x) = \frac{1}{x^2+3x} \)
2000002405
Level:
B
Decide which of the functions is odd.
\( f(x) = \frac{5}{x} \)
\( f(x) = \frac{x^2}{x^2-4} \)
\( f(x) = \frac{x^2}{2-x} \)
\( f(x) =(x+1)^2 \)
2010014502
Level:
B
Let \( f(x)=\frac{\sqrt{x-3}}{x^2-16} \). Which of the statements about the domain of the function \( f \) is true?
\( D(f)=[ 3; 4)\cup (4;\infty) \)
\( D(f)=(3; 4)\cup (4;\infty) \)
\( D(f)=(-\infty; -4)\cup (3;4) \)
\( D(f)=(-4; 3)\cup (4;\infty) \)
2010014507
Level:
B
In the following list identify an even function.
\(f(x)= |x|+1\)
\(f(x)= |x+1|\)
\(f(x)= x+1\)
\(f(x)= x\)
2010014508
Level:
B
In the following list identify a function which is bounded below.
\(f(x) = (x +4)^{2}\)
\(f(x) = -(x - 1)^{2}\)
\(f(x) = -x^{2}+1\)
\(f(x) = -(x - 4)^{2}+2\)
2010014509
Level:
B
Identify a function which has a domain
\((-\infty ;-2)\cup (3;\infty )\).
\(y = \sqrt{ \frac{1}
{(x+2)(x-3)}}\)
\(y = \sqrt{(x+2)(x-3)}\)
\(y = \frac{1}
{(x+2)(x-3)}\)
\(y = (x+2)(x-3)\)
\(y = \sqrt{(x-2)(x+3)}\)
\(y = \frac{1}
{(x-2)(x+3)}\)
9000004802
Level:
B
In the following list identify an even function.
\(f(x)= |x|\)
\(f(x) = |x + 1|\)
\(f(x) = x + 1\)
\(f(x) = x\)
9000004804
Level:
B
In the following list identify an odd function.
\(f(x) = x^{3}\)
\(f(x) = |x^{3}|\)
\(f(x) = x^{4}\)
\(f(x) = |x^{4}|\)
9000004805
Level:
B
In the following list identify a function which is not an odd function.
\(y = x + 3\)
\(y = x^{5}\)
\(y = \frac{3}
{x}\)
\(y = x\)