Solutions
Solutions to Try Its
1. y-intercept ; x-intercepts , and 2. The graph has a zero of –5 with multiplicity 1, a zero of –1 with multiplicity 2, and a zero of 3 with even multiplicity. 3.![Graph of f(x)=(1/4)x(x-1)^4(x+3)^3.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201514/CNX_Precalc_Figure_03_04_0212.jpg)
Solutions to Odd-Numbered Exercises
1. The x-intercept is where the graph of the function crosses the x-axis, and the zero of the function is the input value for which . 3. If we evaluate the function at a and at b and the sign of the function value changes, then we know a zero exists between a and b. 5. There will be a factor raised to an even power. 7. 9. 11. 13. 15. 17. 19. 21. 23. 25. and . Sign change confirms. 27. and . Sign change confirms. 29. and . Sign change confirms. 31. 0 with multiplicity 2, with multiplicity 5, 4 with multiplicity 2 33. 0 with multiplicity 2, –2 with multiplicity 2 35. 37. 39. with multiplicity 2, 0 with multiplicity 3 41. 43. x-intercepts, with multiplicity 2, with multiplicity 1, y-intercept . As , , as , .![Graph of g(x)=(x+4)(x-1)^2.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201515/CNX_Precalc_Figure_03_04_202.jpg)
![Graph of k(x)=(x-3)^3(x-2)^2.](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201517/CNX_Precalc_Figure_03_04_204.jpg)
![Graph of n(x)=-3x(x+2)(x-4).](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/11/25201518/CNX_Precalc_Figure_03_04_206.jpg)