Wertetabelle und Graph einer linearen Funktion
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Exercise:
Gegeben sind die linearen Funktionen fx -fracx quad gx -frac x + frac quad hx -frac x -. abclist abc Vervollständige die folge Wertetabelle. center renewcommandarraystretch. tabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & & & & & & & & & hline gx & & & & & & & & & hline hx & & & & & & & & & hline tabularx center abc Zeichne die Graphen dieser Funktionen in das Koordinatensystem unten links. abc Bestimme die Umkehrfunktionen dieser Funktionen. abclist
Solution:
abclist abc phantom. center renewcommandarraystretch. adjustboxvttabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & bf & bf frac & bf frac & bf frac & bf & bf -frac& bf -frac & bf -frac & bf - hline gx & bf frac& bf frac& bf frac& bf & bffrac &bffrac &bf -frac &bf - &bf -frac hline hx & bf & bf frac & bffrac & bf -frac & bf - & bf -frac &bf -frac & bf-frac &bf - hline tabularx center abc adjustboxvttikzpicturescale. tkzInitxmin-xmaxymin-ymax tkzGridstep. tkzDrawXright tkzDrawYabove tkzFctvery thickdomain-:-.*x tkzText-.gx tkzFctvery thickdomain-:-.*x+. tkzText-.fx tkzFctvery thickdomain-:-.*x- tkzText-hx tkzLabelXYstep tikzpicture abc Wir setzen jeweils die Funktion mit y gleich und lösen dann nach x auf um die Umkehrfunktion zu erhalten. nprvmulticols itemize item edt y fx -frac x uf -: -fracy x f^-y -fracy ed item edt y gx -frac x + frac uf -frac y - frac -fracx uf -: -fracy + frac x f^-y -fracy + frac ed item edt y fx -frac x - uf + y + -frac uf -: -fracy - frac x f^-y -fracy - frac ed itemize nprvmulticols abclist
Gegeben sind die linearen Funktionen fx -fracx quad gx -frac x + frac quad hx -frac x -. abclist abc Vervollständige die folge Wertetabelle. center renewcommandarraystretch. tabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & & & & & & & & & hline gx & & & & & & & & & hline hx & & & & & & & & & hline tabularx center abc Zeichne die Graphen dieser Funktionen in das Koordinatensystem unten links. abc Bestimme die Umkehrfunktionen dieser Funktionen. abclist
Solution:
abclist abc phantom. center renewcommandarraystretch. adjustboxvttabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & bf & bf frac & bf frac & bf frac & bf & bf -frac& bf -frac & bf -frac & bf - hline gx & bf frac& bf frac& bf frac& bf & bffrac &bffrac &bf -frac &bf - &bf -frac hline hx & bf & bf frac & bffrac & bf -frac & bf - & bf -frac &bf -frac & bf-frac &bf - hline tabularx center abc adjustboxvttikzpicturescale. tkzInitxmin-xmaxymin-ymax tkzGridstep. tkzDrawXright tkzDrawYabove tkzFctvery thickdomain-:-.*x tkzText-.gx tkzFctvery thickdomain-:-.*x+. tkzText-.fx tkzFctvery thickdomain-:-.*x- tkzText-hx tkzLabelXYstep tikzpicture abc Wir setzen jeweils die Funktion mit y gleich und lösen dann nach x auf um die Umkehrfunktion zu erhalten. nprvmulticols itemize item edt y fx -frac x uf -: -fracy x f^-y -fracy ed item edt y gx -frac x + frac uf -frac y - frac -fracx uf -: -fracy + frac x f^-y -fracy + frac ed item edt y fx -frac x - uf + y + -frac uf -: -fracy - frac x f^-y -fracy - frac ed itemize nprvmulticols abclist
Meta Information
Exercise:
Gegeben sind die linearen Funktionen fx -fracx quad gx -frac x + frac quad hx -frac x -. abclist abc Vervollständige die folge Wertetabelle. center renewcommandarraystretch. tabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & & & & & & & & & hline gx & & & & & & & & & hline hx & & & & & & & & & hline tabularx center abc Zeichne die Graphen dieser Funktionen in das Koordinatensystem unten links. abc Bestimme die Umkehrfunktionen dieser Funktionen. abclist
Solution:
abclist abc phantom. center renewcommandarraystretch. adjustboxvttabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & bf & bf frac & bf frac & bf frac & bf & bf -frac& bf -frac & bf -frac & bf - hline gx & bf frac& bf frac& bf frac& bf & bffrac &bffrac &bf -frac &bf - &bf -frac hline hx & bf & bf frac & bffrac & bf -frac & bf - & bf -frac &bf -frac & bf-frac &bf - hline tabularx center abc adjustboxvttikzpicturescale. tkzInitxmin-xmaxymin-ymax tkzGridstep. tkzDrawXright tkzDrawYabove tkzFctvery thickdomain-:-.*x tkzText-.gx tkzFctvery thickdomain-:-.*x+. tkzText-.fx tkzFctvery thickdomain-:-.*x- tkzText-hx tkzLabelXYstep tikzpicture abc Wir setzen jeweils die Funktion mit y gleich und lösen dann nach x auf um die Umkehrfunktion zu erhalten. nprvmulticols itemize item edt y fx -frac x uf -: -fracy x f^-y -fracy ed item edt y gx -frac x + frac uf -frac y - frac -fracx uf -: -fracy + frac x f^-y -fracy + frac ed item edt y fx -frac x - uf + y + -frac uf -: -fracy - frac x f^-y -fracy - frac ed itemize nprvmulticols abclist
Gegeben sind die linearen Funktionen fx -fracx quad gx -frac x + frac quad hx -frac x -. abclist abc Vervollständige die folge Wertetabelle. center renewcommandarraystretch. tabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & & & & & & & & & hline gx & & & & & & & & & hline hx & & & & & & & & & hline tabularx center abc Zeichne die Graphen dieser Funktionen in das Koordinatensystem unten links. abc Bestimme die Umkehrfunktionen dieser Funktionen. abclist
Solution:
abclist abc phantom. center renewcommandarraystretch. adjustboxvttabularx.textwidth|Y|Y|Y|Y|Y|Y|Y|Y|Y|Y| hline x & - & - & - & - & & & & & hline hline fx & bf & bf frac & bf frac & bf frac & bf & bf -frac& bf -frac & bf -frac & bf - hline gx & bf frac& bf frac& bf frac& bf & bffrac &bffrac &bf -frac &bf - &bf -frac hline hx & bf & bf frac & bffrac & bf -frac & bf - & bf -frac &bf -frac & bf-frac &bf - hline tabularx center abc adjustboxvttikzpicturescale. tkzInitxmin-xmaxymin-ymax tkzGridstep. tkzDrawXright tkzDrawYabove tkzFctvery thickdomain-:-.*x tkzText-.gx tkzFctvery thickdomain-:-.*x+. tkzText-.fx tkzFctvery thickdomain-:-.*x- tkzText-hx tkzLabelXYstep tikzpicture abc Wir setzen jeweils die Funktion mit y gleich und lösen dann nach x auf um die Umkehrfunktion zu erhalten. nprvmulticols itemize item edt y fx -frac x uf -: -fracy x f^-y -fracy ed item edt y gx -frac x + frac uf -frac y - frac -fracx uf -: -fracy + frac x f^-y -fracy + frac ed item edt y fx -frac x - uf + y + -frac uf -: -fracy - frac x f^-y -fracy - frac ed itemize nprvmulticols abclist
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Lineare Funktionen I by pw