Sovi AI

题目

解题步骤

1. Understand the question

   use end behavior to select the correct function for each graph:
   a. $x^2 - 7x + 9$
   b. $-x^4 + 2x^2$
   c. $-x^3 - x^2 + 2x - 3$
   d. $x^3 - 4x^2$

2. Explanation

   Step1: Identify degree/leading coefficient rules

   For polynomial $f(x)=a_nx^n+...+a_0$:

   • Even $n$: $\lim_{x\to\pm\infty}f(x)=+\infty$ if $a_n>0$; $\lim_{x\to\pm\infty}f(x)=-\infty$ if $a_n<0$
   • Odd $n$: $\lim_{x\to+\infty}f(x)=+\infty, \lim_{x\to-\infty}f(x)=-\infty$ if $a_n>0$; $\lim_{x\to+\infty}f(x)=-\infty, \lim_{x\to-\infty}f(x)=+\infty$ if $a_n<0$

   Step2: Analyze top (green) graph

   End behavior: $x\to+\infty, f(x)\to+\infty$; $x\to-\infty, f(x)\to-\infty$. This matches odd degree, positive leading coefficient.
   Check options: d. $x^3-4x^2$ (degree 3, $a_3=1>0$)

   Step3: Analyze second (red) graph

   End behavior: $x\to\pm\infty, f(x)\to-\infty$. This matches even degree, negative leading coefficient.
   Check options: b. $-x^4+2x^2$ (degree 4, $a_4=-1<0$)

   Step4: Analyze third (orange) graph

   End behavior: $x\to\pm\infty, f(x)\to+\infty$. This matches even degree, positive leading coefficient.
   Check options: a. $x^2-7x+9$ (degree 2, $a_2=1>0$)

   Step5: Analyze bottom (blue) graph

   End behavior: $x\to+\infty, f(x)\to-\infty$; $x\to-\infty, f(x)\to+\infty$. This matches odd degree, negative leading coefficient.
   Check options: c. $-x^3-x^2+2x-3$ (degree 3, $a_3=-1<0$)

3. Final answer

   Top (green) graph: d. $x^3 - 4x^2$
   Second (red) graph: b. $-x^4 + 2x^2$
   Third (orange) graph: a. $x^2 - 7x + 9$
   Bottom (blue) graph: c. $-x^3 - x^2 + 2x - 3$

答案

Question Analysis

OCR Text

use end behavior to select the correct function for each graph:
a. $x^2 - 7x + 9$
b. $-x^4 + 2x^2$
c. $-x^3 - x^2 + 2x - 3$
d. $x^3 - 4x^2$

相关知识点

关联题目

• 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…

• use end behavior to select the correct function for each graph: a. $x^2…

  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. $-x^3 - x^2 + 4x - 3$

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

  none of the graphs shown

Sovi AI iOS

官网：mysovi.ai。题库页面域名：question-banks.mysovi.ai。iOS 应用通过 Apple App Store 提供。