חזקה טבעית של פונקציה – חלק ג – מדרגה 1 – Stepped Tasks

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

מדרגה 1

בסרטוט נתון גרף הפונקציה $h(x)$ .

$h(x)$

תחום הגדרה: כל $x$

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

נקודות קיצון: מינימום $(0.7,-1)$ , $(-0.7,-1)$ מקסימום $(0,0)$

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

תוכלו לבדוק תשובותיכם בעזרת היישומון המצורף.

אחרי שפתרתם את הבעיות במדרגה 1, פתרו את בעיית המטרה.
או, במידת הצורך, פתרו את הבעיות במדרגה 2.

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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