Sovi AI

問題

解法ステップ

1. Understand the question

   use end behavior to select the correct function for each graph:
   a. $x^2 - 8x + 9$
   b. $x^3 - 4x^2$
   c. $-x^3 - x^2 + 4x - 3$
   d. $-x^4 + 2x^2$

2. Explanation

   Step1: Identify degree/leading coefficient for each function

   • a. $x^2 - 8x + 9$: Degree 2 (even), leading coefficient $1>0$
   • b. $x^3 - 4x^2$: Degree 3 (odd), leading coefficient $1>0$
   • c. $-x^3 - x^2 + 4x - 3$: Degree 3 (odd), leading coefficient $-1<0$
   • d. $-x^4 + 2x^2$: Degree 4 (even), leading coefficient $-1<0$

   Step2: Match end behavior to top graph

   Top graph: As $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to+\infty$ (both ends up). Matches even degree, positive leading coefficient: a. $x^2 - 8x + 9$

   Step3: Match end behavior to second graph

   Second graph: As $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to-\infty$ (right up, left down). Matches odd degree, positive leading coefficient: b. $x^3 - 4x^2$

   Step4: Match end behavior to third graph

   Third graph: As $x\to+\infty$, $f(x)\to-\infty$; as $x\to-\infty$, $f(x)\to-\infty$ (both ends down). Matches even degree, negative leading coefficient: d. $-x^4 + 2x^2$

   Step5: Match end behavior to bottom graph

   Bottom graph: As $x\to+\infty$, $f(x)\to-\infty$; as $x\to-\infty$, $f(x)\to+\infty$ (right down, left up). Matches odd degree, negative leading coefficient: c. $-x^3 - x^2 + 4x - 3$

3. Final answer

   Top (orange) graph: a. $x^2 - 8x + 9$
   Second (green) graph: b. $x^3 - 4x^2$
   Third (red) graph: d. $-x^4 + 2x^2$
   Bottom (blue) graph: c. $-x^3 - x^2 + 4x - 3$

答え

Question Analysis

OCR Text

use end behavior to select the correct function for each graph:
a. $x^2 - 8x + 9$
b. $x^3 - 4x^2$
c. $-x^3 - x^2 + 4x - 3$
d. $-x^4 + 2x^2$

関連トピック

関連問題

• use an area model to solve 31 × 26. multiply in the area model.

  Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806

• 6. solve each equation. write each solution as a fraction and as a deci…

  | Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

• Ok

  - Fila 2: Circular el par (5, 2). - Fila 3: Circular el par (3, 3) (o la tarjeta con 3 y la otra con 4 dibujos, pero los números son 3 y 3? Wait, la tercera fila: primera tarjeta …

• How do you solve pemdas

  It's basically just a checklist so you don't get mixed up when a math problem has a bunch of stuff going on at once. You just go down the list in order: 1. **P**arentheses: Do any…

• which number line models $-1 + (-14)$? add. $-1 + (-14) = \\square$

  \(-15\)

• 11 et 12

  The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

• which graphs are inverses of one another?○ graph a and b○ graph a and c…

  none of the graphs shown

• 19. is the inverse of the function $f(x) = -60(x - 3)^2 - 50$ also a fu…

  No, the inverse of $f(x) = -60(x-3)^2 - 50$ is not a function. The original function is a downward-opening parabola, which fails the horizontal line test (horizontal lines interse…

Sovi AI iOS

公式サイトは mysovi.ai。問題ページは question-banks.mysovi.ai で配信。iOS アプリは Apple App Store で提供。