9000005807
Level:
C
Consider the function \(f(x) = -x + 4\)
and a triangle which has one side on the graph of
\(f\) and
two other sides on the axes. Find the area of this triangle.
\(8\)
\(4\)
\(6\)
\(10\)
C
9000005809
Level:
C
Consider the functions \(f(x) = x - 1\)
and \(g(x) y = -x + a\). Find the value
of the real parameter \(a\in \mathbb{R}\)
which ensure that the functions have a common value at
\(x = 3\), i.e.
\(f(3) = g(3)\).
\(a = 5\)
\(a = -1\)
\(a = 1\)
\(a = 2\)
9000007201
Level:
C
Consider the function
\[
f(x) = [x + 2]
\]
defined on the domain \(\mathop{\mathrm{Dom}}(f) = (1;2)\).
Find the parameters \(a\)
and \(b\)
in the linear function
\[
g(x) = ax + b
\]
which ensure that the functions \(f\)
and \(g\) are identical
on the domain of \(f\).
\[ \]
Hint: The function \(y = [x]\)
is a floor function: the largest integer less than or equal to
\(x\). For positive
\(x\) it is also called the
integer part of \(x\).
\(a = 0\),
\(b = 3\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 3\),
\(b = 0\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 0\),
\(b = 4\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = -3\),
\(b = 0\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
9000005810
Level:
C
Consider the functions \(f(x) = x + 1\)
and \(g(x) = ax + 7\). For what values of the real parameter \(a\in \mathbb{R}\),
do the functions have the same function value equal to \(3\).
\(a = -2\)
\(a = -7\)
\(a = -1\)
\(a = 7\)
9000007105
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) share
only ....”
the solution set \(K\)
the value of the coefficient \(a\)
the value of the coefficient \(b\)
the value of the coefficient \(c\)
9000007103
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) share
only ....”
the value of the coefficient \(a\)
the value of the coefficient \(b\)
the value of the coefficient \(c\)
the solution set \(K\)
9000007104
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) share
only ....”
the value of the coefficient \(b\)
the value of the coefficient \(a\)
the value of the coefficient \(c\)
the solution set \(K\)
9000007102
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) differ
only in ....”
the coefficient \(c\)
the coefficient \(a\)
the coefficient \(b\)
the solution set \(K\)
9000007101
Level:
C
Consider a family \(M\)
of quadratic functions, as shown in the picture. Any quadratic function in this family
is given by the analytic expression
\[
y = ax^{2} + bx + c
\]
where \(a\),
\(b\) and
\(c\) are real constants and
\(a\not = 0\). For each function
the set \(K\) denotes the
set of \(x\)-intercepts. Complete the statement. „The analytic expressions for functions in the family
\(M\) differ
only in ....”
the coefficient \(a\)
the coefficient \(b\)
the coefficient \(c\)
the set \(K\)
9000004905
Level:
C
In the following list identify a statement which is not true for the function
\(f\colon y = |\log (x - 3) - 1|\).
The function \(f\)
is increasing on the domain.
The domain of the function \(f\)
is \((3;\infty )\).
All values of the function \(f\)
are nonnegative.
The function \(f\) does
not have a \(y\)-intercept.
The \(x\)-intercept
of the function \(f\)
is \(x = 13\).
The function \(f\)
is not one-to-one.