9000007802
Level:
A
Consider linear functions \(f(x) = ax - 2\)
and \(g\colon y = -4x + 3\). Find the value of
the real parameter \(a\) which
ensure that the graphs of \(f\)
and \(g\)
are two parallel lines.
\(- 4\)
\(4\)
\(- 2\)
\(2\)
Linear Functions
9000007804
Level:
A
Three of the points \(A = [2;-4]\),
\(B = [0;-3]\),
\(C = [-2;-1]\),
\(D = [-4;1]\) lie on
the graph of the same linear function. Identify these points. (Colinear points.)
\(B\),
\(C\),
\(D\)
\(A\),
\(B\),
\(C\)
\(A\),
\(B\),
\(D\)
\(A\),
\(C\),
\(D\)
9000007808
Level:
B
Given a function \(f(x) = \frac{x}
{3} + 1\), find
the function \(g\) such that
the graph of \(g\) is symmetric
with the graph of \(f\)
about the \(y\)-axis.
\(g\colon y = -\frac{x}
{3} + 1\)
\(g\colon y = 3x + 1\)
\(g\colon y = -3x + 1\)
\(g\colon y = -\frac{x}
{3} - 1\)
Such a function does not exist.
9000007809
Level:
C
The price of a goods in a shop is \(\$15\)
per item. The Internet price in an e-shop is cheaper by
\(\$2\) per item. The shipping
cost of the e-shop is \(\$125\).
What is the minimal number of items, which makes the total cost for a transaction
smaller in the e-shop?
\(63\)
\(9\)
\(62\)
\(125\)
\(126\)
9000007810
Level:
C
A fuel tank in a car has the capacity \(40\)
litres. The current volume of the fuel in the fuel tank is
\(6\) litres. The speed
of fuelling is \(1\) litre
of gasoline each \(3\)
seconds. Find the function which describes the volume of the gasoline in the fuel tank (in litres)
as a function of time (in seconds).
\(V = \frac{1}
{3}t + 6,\ t\in [ 0;102] \)
\(V = 3t + 6,\ t\in [ 0;102] \)
\(V = 3t + 6,\ t\in [ 0;40] \)
\(V = 3t + 6,\ t\in \mathbb{R}_{0}^{+}\)
\(V = \frac{1}
{3}t + 6,\ t\in [ 0;40] \)
9000009301
Level:
C
An automatic machine produces \(12\)
components per minute and stores them in a box with capacity
\(1\: 500\)
components. The machine starts with an initial amount of
\(240\)
components in the box. In what time will be the box full?
\(1\, \mathrm{h}\)
\(45\, \mathrm{min}\)
\(1\, \mathrm{h}\)
\(55\, \mathrm{min}\)
\(2\, \mathrm{h}\)
\(5\, \mathrm{min}\)
\(2\, \mathrm{h}\)
\(15\, \mathrm{min}\)
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.
\(g(x) = -x\)
\(g(x)= x\)
\(g(x) = x + 1\)
\(g(x) = x - 1\)
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.
\([3;0]\)
\([0;-6]\)
\([0;-4]\)
\([6;0]\)
9000005707
Level:
A
Let \(f\) be the linear
function \(f(x) = -x + 4\) restricted
to the interval \(x\in [ - 3;2] \).
Find the range of \(f\).
\([ 2;7] \)
\([ 1;6] \)
\([ - 3;3] \)
\([ - 1;2] \)
9000005710
Level:
A
Consider the linear function \(f(x) = 4x + 4\).
Find the intersection point of the graph of
\(f\) with
\(y\)-axis.
\([0;4]\)
\([-1;0]\)
\([-4;0]\)
\([0;0]\)