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3.1E: Power Functions (Exercises)

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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?

23.24.25.26.

27. 28.29.30.

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

$179$