# 9. graph

Example 1: f(x) = x^{4} + 8x^{3} + 22x^{2} + 24x + 9

•1. Domf = R

•2. f is continuous and derivable in** R** because it is a polynomial function.

•3. Symmetry: f is a function which is neither odd nor even.

•4. f is not a periodic function.

•5. intersection points: (-3,0),(-1,0),(0,9)

•6. There are no asymptotes because it is a polynomial function.

•7. f’(x) = 4x^{3} + 24x^{2} + 44x + 24 f’(x) = 0 ↔ x Є {-3, -2, -1}

^{2}+ 48x + 44 f’’(x) = 0 ↔ x ≈ -2.58, -1.42

Example 2: f(x) = x^{3} + 3x^{2} - 4

•1. Domf = **R**

•2. f is continuous and derivable in **R** because it is a polynomial function.

•3. Symmetry: f is a function which is neither odd nor even.

•4. f is not a periodic function.

•5. intersection points: (-2,0),(1,0),(0,-4)

•6. There are no asymptotes because it is a polynomial function.

•7. f’(x) = 3x^{2} + 6x

f’(x) = 0 ↔ x Є {-2, 0}

f’’(x) = 0 ↔ x =-1

Example 3:

**R**– {-2,2}

**Exercise**: draw the graphs of the functions:

^{4}- 2x

^{2}- 8

^{x}

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