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題目

解題步驟

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

答案

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

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