2010012601
Level:
A
Find the area of the region bounded by the curves
\(y =\mathrm{e} ^{x}-1\),
\(y = -\mathrm{e}^{x} + 1\) and
\(x = 1\).
\(2\mathrm{e}-4 \)
\(2\mathrm{e}-2\)
\(2\)
\(4-2\mathrm{e} \)
A
2010012505
Level:
A
Identify a true statement about the function
\(f(x) = -\frac{3}
{4}x^{4} +2x^{3}\).
The function \(f\) has
a local maximum at \(x = 2\).
The function \(f\) has
a local minimum at \(x = 0\).
The function \(f\)
has two local extrema. These extrema are at
\(x = 0\) and
\(x = 2\).
The function \(f\)
has neither local minimum nor local maximum.
2010012406
Level:
A
Find the false statement about the function \( f(x)=(x-2)^4-3 \).
The function \( f \) is even.
The function \( f \) has the minimum at \( x=2 \).
The function \( f \) is bounded below.
The range of the function \( f \) is the interval \( [ -3;\infty) \).
2010012405
Level:
A
Find the true statement about the function \( f(x)=(x+1)^3-2 \).
The function \( f \) is an injective (one-to-one) function.
The function \( f \) is decreasing.
The function \( f \) is odd.
The function \( f \) has the minimum at \( x=-1 \).
2010012404
Level:
A
In the following list identify a decreasing function.
\(f \colon y =-x^{3}\)
\(f \colon y = x^{4}\)
\(f \colon y = -x^{4}\)
\(f \colon y = x^{-3}\)
\(f \colon y = -x^{2}\)
2010012403
Level:
A
Identify a function which is not one-to-one on the interval
\([ - 2;2 ] \).
\(f \colon y = x^{2}-2\)
\(f \colon y = x^{2}+4x\)
\(f \colon y = -x^{3}\)
\(f \colon y = (x - 2)^{2}\)
\(f \colon y = (x +2)^{2}\)
\(f \colon y = x^{3}-2\)
2010012402
Level:
A
Identify a function which is decreasing on
\((-3;2 )\).
\(f \colon y = (x - 2)^{2}\)
\(f \colon y = (x + 2)^{2}\)
\(f \colon y = (x +3)^{2}\)
\(f \colon y = x^{2}-2x\)
\(f \colon y =-x^{2}+1\)
\(f \colon y = x^{3}\)
2010012401
Level:
A
Identify a function which is increasing on
\((-1;\infty )\).
\(f\colon y = x^{3}\)
\(f\colon y= x^{4}\)
\(f\colon y= -x^{3}\)
\(f\colon y = x^{-4}\)
\(f\colon y =- x^{-2}\)
\(f\colon y = -x^{-3}\)
2010012304
Level:
A
Let \( f(x)=-x^2 \). Given the graph of the function \( f \) and the graph of a function \( g \) which was obtained as a vertical shift of the graph of \( f \) (see the picture), choose the function \( g \).
\( g(x) = -x^2+2 \)
\( g(x) = (x-2)^2 \)
\( g(x) = -x^2-2 \)
\( g(x) = (x+2)^2 \)
2010012303
Level:
A
Find the \(y\)-intercept
of the following function. \[f(x) = 6x^{2} +12x - 7.2\]
\([0;-7.2]\)
\([-7.2;0]\)
\([6;0]\)
There is no \(y\)-intercept.