חזקה טבעית של פונקציה – חלק ג – בעיית מטרה – Stepped Tasks

חזקה טבעית של פונקציה - חלק ג' - $f^n{(x)}$

בעיית מטרה

בסרטוט נתון גרף הפונקציה $f(x)$ .

$f(x)$

תחום הגדרה: כל $x$

נקודות חיתוך עם הצירים: $(1,0)$ , $(0,0)$ , $(-2,0)$

נקודות קיצון: מקסימום $(-1.2,2.1)$ , מינימום $(0.5,-0.6)$

סרטטו באותה מערכת צירים, בצבעים שונים, את הגרפים של:
א. $f^3(x)$
ב. $f^2(x)$
באיזה תחום $f^3(x)\le{f^2(x)}$ ? (דייקו בתשובתכם ככל האפשר).
תוכלו לבדוק תשובותיכם בעזרת היישומון המצורף.
לאיזו פונקציה מבין הפונקציות $f^3(x)$ , $f^2(x)$ , $f(x)$ יש נקודות פיתול בהן שיפוע המשיק הוא אפס?
מה הם שיעורי נקודות אלה?

במידת הצורך פתרו את הבעיות במדרגה 1.

מתוך מחסן הנקודות יש לגרור ולמקם לפחות שבע נקודות כחולות (לסרטוט $f^2(x)$ ) ולפחות שבע נקודות צהובות (לסרטוט $f^3(x)$ ), במקומות המתאימים להן.
יש להיעזר בעיפרון שבתפריט העליון, ולסרטט את גרף הפונקציה החדשה.
ניתן לבצע בדיקה רק לאחר מיקום של לפחות שבע נקודות מכל אחד מהצבעים.
במידת הצורך, ניתן להציג שיקוף של הנקודה האדומה על ידי בחירה של האפשרות המתאימה בתפריט שבתחתית היישומון: שיקוף בציר ה- $x$ או בציר ה- $y$ .
כדי "לנקות" את היישומון ולהתחיל מחדש עם הפונקציה המוצגת, ניתן ללחוץ על אתחול.

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