9000028107
Level:
B
Given graphs of the linear functions \(f\)
and \(g\), find the solution
set of the inequality \(f(x)\leq g(x)\).
\(\mathbb{R}\)
\(\emptyset \)
\((-\infty ;0] \)
\([ 0;\infty )\)
Linear functions
9000028108
Level:
B
Given graph of the linear function \(f\),
find the solution set of the inequality \(f(x) < 0\).
\(\emptyset \)
\((-\infty ;0] \)
\(\mathbb{R}\)
\([ 0;\infty )\)
9000028109
Level:
B
Given graphs of the linear functions \(f\),
\(g\) and
\(h\), find the solution set
of the inequality \(f(x)\leq g(x) < h(x)\).
\((3.73;\infty )\)
\([ - 1.04;1)\)
\((1;\infty )\)
\([ 1;3.73)\)
9000028110
Level:
B
Given graphs of linear functions \(f\),
\(g\) and
\(h\), find the solution set
of the inequality \(f(x)\leq g(x) < h(x)\).
\([ 4;7)\)
\((-\infty ;4] \)
\([ 1;7)\)
\([ 7;\infty )\)
1003160901
Level:
C
Suppose \( f \) is a linear function. If the value of the independent variable \( x \) increases by \( 6 \), the function value increases by \( 18 \). Choose the correct form of the function \( f \), such that the given property is preserved.
\( f(x)=3x+1 \)
\( f(x)=-3x \)
\( f(x)=\frac13x+18 \)
\( f(x)=\frac13x \)
1003160902
Level:
C
Suppose \( f \) is a linear function. If the value of the independent variable \( x \) increases by \( 4 \), the function value decreases by \( 12 \). Choose the correct form of the function \( f \), such that the given property is preserved.
\( f(x)=-3x \)
\( f(x)=3x \)
\( f(x)=3x-12 \)
\( f(x)=-\frac13x \)
1003160903
Level:
C
The graph of a linear function \( f \) passes through the point \( \left[4\sqrt3;2\right] \) and it makes an angle of \( 30^{\circ} \) with the positive direction of \( x \)-axis measured anticlockwise. Choose the correct form of the function \( f \), such that the given property is preserved.
\( f(x)=\frac{\sqrt3}3x-2 \)
\( f(x)=\sqrt3x-10 \)
\( f(x)=\frac{\sqrt3}3x+2 \)
\( f(x)=\sqrt3x+10 \)
1003171301
Level:
C
The freezing point and the boiling point of water (both under the normal atmospheric pressure) are the base of the most commonly used temperature scale around Europe. It is Celsius temperature scale in Celsius degrees (\( ^{\circ}\mathrm{C} \)). Fahrenheit temperature scale in Fahrenheit degrees (\( ^{\circ}\mathrm{F} \)) is of general common use in English speaking countries especially in the USA. The basic temperature points in mentioned scales have the values:
\[ \begin{array}{l}
\text{Water freezing point } \dots\ 0\,^{\circ}\mathrm{C} / 32\,^{\circ}\mathrm{F} \\
\text{Water boiling point } \dots\ 100\,^{\circ}\mathrm{C} / 212\,^{\circ}\mathrm{F}
\end{array} \]
From the following equations choose the one that can be used to convert a temperature from its Celsius representation to the Fahrenheit value, provided you know that the relationship between the scales is linear. (In equations, \( F \) is a numerical value of a temperature in Fahrenheits and \( C \) is a numerical value of a temperature in Celsius.)
\( F=\frac95 C+32 \)
\( F=\frac59C+32 \)
\( F=\frac59 C-\frac{160}9 \)
\( F=32C+100 \)
1003171601
Level:
C
Consider the function \( f \) given by \( f(x)=\frac12x+\frac32 \) and consider the line \( p \) that is parallel to the \( x \)-axis and intersects \( y \)-axis at the point \( \left[0;\frac12\right] \). Find the function \( g \) such that the graph of \( g \) is symmetric with the graph of \( f \) about the line \( p \).
\( g(x)=-\frac12x-\frac12 \)
\( g(x)=2x-\frac12 \)
\( g(x)=-\frac12x-\frac32 \)
\( g(x)=\frac12x-\frac32 \)
1103171201
Level:
C
Suppose a train comes to stop uniformly. The instantaneous velocity \( v \) of the train in the time \( t \) of slowing down is modelled by \( v=45-25t \). Find the graph of the function \( v \).
