Questions: Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. Drag each graph given above into the area below the appropriate function, depending on which graph is represented by which function. 15. f(x)=-x^4+x^2 16. f(x)=x^3-2x^2 17. f(x)=(x-2)^2 18. f(x)=-x^3-x^2+4x-5

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph.

Drag each graph given above into the area below the appropriate function, depending on which graph is represented by which function.

15. f(x)=-x^4+x^2
16. f(x)=x^3-2x^2
17. f(x)=(x-2)^2
18. f(x)=-x^3-x^2+4x-5
Transcript text: Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. Drag each graph given above into the area below the appropriate function, depending on which graph is represented by which function. 15. $f(x)=-x^{4}+x^{2}$ 16. $f(x)=x^{3}-2 x^{2}$ 17. $f(x)=(x-2)^{2}$ 18. $f(x)=-x^{3}-x^{2}+4 x-5$ $\square$ $\square$ $\square$ $\square$
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Solution

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Solution Steps

Step 1: Analyze f(x) = -x⁴ + x²

The leading term is -x⁴. The degree is 4 (even), and the leading coefficient is -1 (negative). Therefore, the end behavior is down and down (as x approaches negative infinity, f(x) approaches negative infinity; as x approaches positive infinity, f(x) approaches negative infinity). This corresponds to the graph in the top right.

Step 2: Analyze f(x) = x³ - 2x²

The leading term is x³. The degree is 3 (odd), and the leading coefficient is 1 (positive). Therefore, the end behavior is down and up (as x approaches negative infinity, f(x) approaches negative infinity; as x approaches positive infinity, f(x) approaches positive infinity). This corresponds to the graph in the bottom right.

Step 3: Analyze f(x) = (x - 2)²

This simplifies to f(x) = x² - 4x + 4. The leading term is x². The degree is 2 (even) and the leading coefficient is 1 (positive). Therefore, the end behavior is up and up (as x approaches negative infinity, f(x) approaches positive infinity; as x approaches positive infinity, f(x) approaches positive infinity). This corresponds to the graph in the top left.

Final Answer:

  1. Top Right Graph
  2. Bottom Right Graph
  3. Top Left Graph
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