1003019301
Level:
B
Which of the following functions has maximum at \( x=-3 \)?
\( f(x) = -2x-3;\ x\in[-3;3)\)
\( h(x) = 2x+3;\ x\in[-3;3]\)
\( g(x) = -3x+2;\ x\in(-3;3]\)
\( m(x) = 2x-3;\ x\in(-\infty;0]\)
Properties of functions
9000033703
Level:
B
Find the domain of the following function.
\[
f\colon y = \frac{x}
{\sqrt{4x^{2 } - 9}}
\]
\(\left (-\infty ;-\frac{3}
{2}\right )\cup \left (\frac{3}
{2};\infty \right )\)
\(\mathbb{R}\)
\(\mathbb{R}\setminus \left \{-\frac{3}
{2}; \frac{3}
{2}\right \}\)
\(\left (-\frac{3}
{2}; \frac{3}
{2}\right )\)
\(\left [ -\frac{3}
{2}; \frac{3}
{2}\right ] \)
\(\left (-\infty ;-\frac{3}
{2}\right ] \cup \left [ \frac{3}
{2};\infty \right )\)
9000021808
Level:
B
Find the domain of the following function.
\[
f(x) = \sqrt{\frac{(x - 3)(x + 2)}
{(1 - x)(3 - x)}}
\]
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;3)\cup (3;\infty )\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2)\cup (1;3)\)
\(\mathop{\mathrm{Dom}}(f) = (-\infty ;-2] \cup (1;\infty )\)
\(\mathop{\mathrm{Dom}}(f) =[ -2;1)\cup (3;\infty )\)
9000010603
Level:
B
Identify a function which has a domain
\(\left (-\infty ;-\frac{3}
{2}\right ] \).
\(y = \sqrt{-2x - 3}\)
\(y = \sqrt{3x + 2}\)
\(y = -\sqrt{2 - 3x}\)
\(y = \sqrt{x + \frac{3}
{2}}\)
\(y = \sqrt{x^{2 } - 3x}\)
\(y = \frac{1}
{3x+2}\)
9000010609
Level:
C
Identify a function which is a possible inverse to the function graphed in the
picture.
\(y = x^{-1}\),
\(x\in (0;\infty )\)
\(y = x\),
\(x\in (0;\infty )\)
\(y = -x\),
\(x\in (0;\infty )\)
\(y = -x^{-1}\),
\(x\in (0;\infty )\)
\(y = x^{2}\),
\(x\in (0;\infty )\)
\(y = -x^{2}\),
\(x\in (0;\infty )\)
9000010610
Level:
C
Identify a function which is a possible inverse to the function graphed in the
picture.
\(y = x^{2}\),
\(x\in (-\infty ;0] \)
\(y = x^{-2}\),
\(x\in (-\infty ;0] \)
\(y = -x^{2}\),
\(x\in [ 0;\infty )\)
\(y = x^{\frac{1}
{2} }\),
\(x\in [ 0;\infty )\)
\(y = -x^{\frac{1}
{2} }\),
\(x\in [ 0;\infty )\)
\(y = -2x\),
\(x\in (-\infty ;0] \)
9000010608
Level:
C
Identify a function which is a possible inverse to the function graphed in the
picture.
\(y = x^{3}\),
\(x\in (-\infty ;\infty )\)
\(y = x^{-3}\),
\(x\in (-2;2)\)
\(y = x^{\frac{1}
{3} }\),
\(x\in (0;\infty )\)
\(y = -x^{\frac{1}
{3} }\),
\(x\in (-\infty ;\infty )\)
\(y = 8x\),
\(x\in (-\infty ;\infty )\)
\(y = -4x\),
\(x\in (-\infty ;\infty )\)
9000010604
Level:
B
Identify a function which has a domain
\([ - 3;5)\).
\(y = \sqrt{\frac{x+3}
{5-x}}\)
\(y = \sqrt{(x - 3)(x + 5)}\)
\(y = \sqrt{\frac{x-5}
{x+3}}\)
\(y = \sqrt{(x - 5)(x + 3)}\)
\(y =\log \frac{x+5}
{x-3}\)
\(y =\log \frac{x+3}
{x-5}\)
9000010602
Level:
B
Identify a function which has a domain
\((-\infty ;-2)\cup (2;\infty )\).
\(y = \sqrt{ \frac{1}
{x^{2}-4}}\)
\(y = \frac{1}
{x^{2}-4}\)
\(y = \sqrt{x^{2 } + 4}\)
\(y = \sqrt{x^{2 } - 2}\)
\(y = \sqrt{x^{2 } - 4}\)
\(y = \sqrt{ \frac{1}
{x^{2}-2}}\)
9000010601
Level:
B
Identify a function which has a domain
\([ - 3;1] \).
\(y = \sqrt{-x^{2 } - 2x + 3}\)
\(y = \sqrt{-x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } + 2x - 3}\)
\(y = \sqrt{x^{2 } - 2x + 3}\)
\(y = \sqrt{\frac{x+3}
{x+1}}\)
\(y = \sqrt{\frac{x-1}
{x+3}}\)