אסימפטוטות או "חורים" בפונקציות מנה – חלק א – בעיית מטרה – Stepped Tasks

אסימפטוטות או "חורים" בפונקציות מנה - חלק א'

בעיית מטרה

נתונה משפחת הפונקציות: $g(x)=\Large\frac{x^2-2x+c}{x^2-4x}$ , $c$ פרמטר.

מצאו במשפחה הנתונה, במידת האפשר, בהתאם לערכים שונים של הפרמטר, פונקציות:

בעלות שתי אסימפטוטות מאונכות לציר x וללא נקודות חיתוך עם ציר ה-x.
בעלות שתי אסימפטוטות מאונכות לציר x ושתי נקודות חיתוך עם ציר ה-x.
בעלות שתי אסמפטוטות מאונכות לציר x ונקודת חיתוך אחת עם ציר ה-x.
בעלות אסימפטוטה אנכית אחת בלבד וללא נקודת אי-הגדרה נוספת.
בעלות אסימפטוטה אנכית אחת בלבד ונקודת אי הגדרה נוספת.
ללא אסימפטוטה אנכית כלל.
בחקירתכם: תוכלו לבדוק תשובותיכם באמצעות היישומון המצורף.
השלימו חקירה עד לקבלת סקיצה לגרף עבור: $g(x)=\Large\frac{x^2-2x+c}{x^2-4x}$
במקרים הבאים: $c=-8$ , $c=0$ .

במידת הצורך פתרו את הבעיות במדרגה 1.

קבעו ערך מספרי לפרמטר $c$ ולחצו $Enter$ .
ניתן להציג אסימפטוטות.

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