Math Problem Statement
welche sind korrekt
Solution
To analyze the### Lösung zu image Beispiel 9:
Anhand des Graphen:
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solution . Diese Here's Aussage what ist I korrekt, interpret based da on your der Graph image:
Be derispiel Funktion für9:
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correct2 statements. from Aussage the: following ** options":
f1 hat. nur ( einfache f Null \stellen)." is** positive
in the Diese interval Aussage ist ( falsch4,, da bei8 \() x \ = 2.
)2 der. Graph ( die f x -A)chse berührt, was auf has eine doppelte three Nullstelle roots ( hzero pointsindeutet.
3).
3.. ( f Aussage :) **"f( has only simple roots.
42.) ( = f0."(**12
) = Diese Aussage0 ist \ korrekt).
,From da the der Graph bei die x-Achse berührt.
Lösung zu Beispiel graph shown10, we can observe:
:
- The function1 crosses the ( x .)-axis three Aussage times, so there: are three roots (zero points).
- At each ** root, the function crosses the axis rather than" touching it and turning backf, meaning all roots are(x) ** >simple roots0**.
- für alle ( x \ In thein (- interval2 (; ( 41) ,)."**
Diese8 Aussage ist falsch), da \ der), Graph the im function is Intervall ( (- negative,2 not; positive. 1-) From the \ graph,) auch ( f( unter12halb) der x -Achneq se liegt0.
\2);. it Aussage does: not ** pass" throughf the( (1) x \ =)- axis0." at** ( x =
Diese Aussage12 ist \ korrekt).
,** daCorrect der answers Graph for Beispiel bei9 (: x** =- f1 \) has die three roots (zero points).
- has only simple roots x.
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zuThe meiner Lösung problem oder appears Details to ask? about
the sign### Verwand ofte ( Fragen f:
(x1). ) and Was its ist behavior eine in dopp the givenelte interval Null.
stelleFrom, the graph:
- Graph foren all? (
x2 . Wie bestimmtin man (- das2 Vor,zeichen einer1 Funktion) in einem Intervall? \
), as the curve lies above the (3. x Welche \ Bedingungen gelten für)- Nullaxisstellen in in this Polyn rangeomen. dritten- ( Grades f(?1
) = 04 .), as Wie interpre thetiert man den Verlauf einer Funktion in Bezug auf ihr Polynomgrad?
- Was sind typische Eigenschaften von Polynomen dritten Grades?
Tipp: Kontrolliere die Berühr- oder Schnittpunkte einer Funktion mit der x-Achse, um Nullstellenarten zu bestimmen. function crosses the -axis at .
Correct answers for Beispiel 10:
- for all .
- .
Summary:
- For Beispiel 9: Options 2 and 3 are correct.
- For Beispiel 10: Options 1 and 2 are correct.
Would you like further explanations or have any specific questions about these problems?
Here are 5 related questions for you to consider:
- What is the difference between simple and multiple roots in a polynomial?
- How can you determine the degree of a polynomial from its graph?
- How do intervals of positivity and negativity relate to the graph of a function?
- What are the steps to identify roots from a graph?
- How does the behavior of a function at its roots depend on their multiplicity?
Tip: When analyzing graphs, always observe where the function crosses or touches the -axis and how it behaves in different intervals!
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Math Problem Analysis
Mathematical Concepts
Polynomial Functions
Roots of Polynomials
Graph Analysis
Formulas
No specific formula; analysis is based on graph interpretation.
Theorems
Multiplicity of roots
Sign changes in intervals of polynomials
Suitable Grade Level
Grades 10-12
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