9000005805
Level:
B
Consider the linear function \(f(x) = x\).
Identify a linear function \(g\)
such that the graphs of \(f\)
and \(g\) are symmetric
about the \(x\)-axis.
\(g(x) = -x\)
\(g(x)= x\)
\(g(x) = x + 1\)
\(g(x) = x - 1\)
Linear Functions
9000005708
Level:
A
Consider the linear function \(f(x)= -5x + 4\)
and points \(A = [1,-1]\),
\(B = [-2,-14]\),
\(C = [3,-11]\),
\(D = [-4,24]\).
How many of these points lies on the graph of the function
\(f\)?
\(3\)
\(1\)
\(2\)
\(4\)
9000005802
Level:
A
Given the linear function \(f(x) = -\frac{1}
{4}x + 4\),
evaluate
\[
f(2a)\cdot f(-2a).
\]
\(16 -\frac{a^{2}}
{4} \)
\(0\)
\(4 - a^{2}\)
\(- 4 + a^{2}\)
9000005709
Level:
A
Consider the linear function \(f(x)= -\frac{4}
{3}x + 4\).
Find the intersection point of the graph of
\(f\) with
\(x\)-axis.
\([3,0]\)
\([0,-6]\)
\([0,-4]\)
\([6,0]\)
9000005808
Level:
C
Consider the linear functions \(f(x) = x\),
\(g(x) = -x\) and
\(h(x)= 3\).
Consider also a triangle which is formed by the graphs of these three functions. Find
the area of this triangle.
\(9\)
\(3\)
\(5\)
\(7\)
9000005710
Level:
A
Consider the linear function \(f(x) = 4x + 4\).
Find the intersection point of the graph of
\(f\) with
\(y\)-axis.
\([0,4]\)
\([-1,0]\)
\([-4,0]\)
\([0,0]\)
9000004210
Level:
A
The function \(g\) is
graphed in the picture. Find \(g(0)\).
\(0\)
\(3\)
\(- 2\)
\(1\)
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 \(x\).
\(a = 0\),
\(b = 3\),
\(\mathop{\mathrm{Dom}}(g) = (1,2)\)
\(a = 3\),
\(b = 0\),
\(\mathop{\mathrm{Dom}}(g) = (1,2)\)
\(a = 0\),
\(b = 4\),
\(\mathop{\mathrm{Dom}}(g) = (1,2)\)
\(a = -3\),
\(b = 0\),
\(\mathop{\mathrm{Dom}}(g) = (1,2)\)
9000005705
Level:
A
Let \(f(x) = -\frac{1}
{2}x + a\). Which value of
the real parameter \(a\) in the
definition of the function \(f\)
guarantees \(f(2) = 2\)?
\(3\)
\(1\)
\(- 4\)
\(5\)
9000005803
Level:
A
Identify an analytic expression of a linear function
\(f\) which
satisfies \(f(-2) = 5\)
and \(f(4) = 2\).
\(f\colon y = -\frac{1}
{2}x + 4\)
\(f\colon y = x - 2\)
\(f\colon y = -x + 6\)
\(f\colon y = -2x + 1\)