Linear functions

9000007209

Level:

A current-voltage characteristics is shown in the graph. Find the current $I$ as a function of the voltage $U$.

$I = \frac{2} {3}U -\frac{4}{3};U\in [2;\infty) $

$I = \frac{3} {2}U - 2;U\in [2;\infty) $

$I = \frac{3} {2}U + 2;U\in [2;\infty) $

$I = \frac{2} {3}U + 2;U\in [2;\infty) $

9000007802

Level:

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.

$- 4$

$4$

$- 2$

$2$

9000007804

Level:

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:

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.

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:

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] $

9000005804

Level:

Given the linear function $f(x) = 5x - 3$, solve the following equation. \[ f(x) = 5a + 2 \]

$x = a + 1$

$x = a$

$x = a + 5$

$x = a - 1$

9000005706

Level:

Let the function $f$ be defined as a linear function with graph passing through the points $A = [2;3]$ and $B = [-1;6]$. Find an analytic expression for the function $f$.

$f(x)= -x + 5$

$f(x) = x + 1$

$f(x)= 2x - 1$

$f(x) = -5x + 1$

9000005805

Level:

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:

Consider the linear function $f(x)= -\frac{4} {3}x + 4$. Find the intersection point of the graph of $f$ with $x$-axis.

$[3;0]$

$[0;-6]$

$[0;-4]$

$[6;0]$

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