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Mathematics LibreTexts

3.1E: Power Functions (Exercises)

[ "article:topic", "license:ccbysa", "showtoc:no", "authorname:lippmanrasmussen" ]
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    13889
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    Find the long run behavior of each function as \(x\to \infty\) and \(x\to -\infty\) \[1. f\left(x\right)=x^{4} 2. f\left(x\right)=x^{6} 3. f\left(x\right)=x^{3} 4. f\left(x\right)=x^{5}\] \[5. f\left(x\right)=-x^{2} 6. f\left(x\right)=-x^{4} 7. f\left(x\right)=-x^{7} 8. f\left(x\right)=-x^{9}\]

    Find the degree and leading coefficient of each polynomial \[9. 4x^{7} 10. 5x^{6}\] \[11. 5-x^{2} 12. 6+3x-4x^{3}\] \[13. -2x^{4} -\; 3x^{2} +\; x-1\; 14. 6x^{5} -2x^{4} +\; x^{2} +\; 3\] \[15. \left(2x+3\right)\left(x-4\right)(3x+1) 16. \left(3x+1\right)\left(x+1\right)(4x+3)\]

    Find the long run behavior of each function as \(x\to \infty\) and \(x\to -\infty\) \[17. -2x^{4} -\; 3x^{2} +\; x-1\; 18. 6x^{5} -2x^{4} +\; x^{2} +\; 3\] \[19. 3x^{2} +\; x-2 20. -2x^{3} +\; x^{2} -x+3\]

    21. What is the maximum number of x-intercepts and turning points for a polynomial of degree 5?

    22. What is the maximum number of x-intercepts and turning points for a polynomial of degree 8?

    What is the least possible degree of the polynomial function shown in each graph?

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    Find the vertical and horizontal intercepts of each function. \[31. f\left(t\right)=2\left(t-1\right)\left(t+2\right)(t-3) 32. f\left(x\right)=3\left(x+1\right)\left(x-4\right)(x+5)\] \[33. g\left(n\right)=-2\left(3n-1\right)(2n+1) 34. k\left(u\right)=-3\left(4-n\right)(4n+3)\]

    \[179\]