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Graph Cubic Functions Lesson 3.1 Page 126

Graph Cubic Functions Lesson 3.1 Page 126. Vocabulary :. A cubic function is a nonlinear function that can be written in the standard form y = ax 3 + bx 2 + cx + d where a ≠ 0. A function f is an odd function if f (- x ) = - f ( x ).

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Graph Cubic Functions Lesson 3.1 Page 126

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  1. Graph Cubic FunctionsLesson 3.1Page 126

  2. Vocabulary: • A cubic functionis a nonlinear function that can be written in the standard form y =ax3 + bx2 + cx + d where a ≠ 0. • A function f is an odd functionif f (-x) = -f (x). • The graphs of odd functions are symmetric about the origin. • A function f is an even functionif f (-x) = f (x). • The graphs of even functions are symmetric about the y-axis.

  3. Even Function Y – Axis SymmetryFold the y-axis (x, y)  (-x, y) (x, y)  (-x, y)

  4. Test for an Even Function • A function y = f(x) is even if , for each x in the domain of f. f(-x) = f(x) Symmetry with respect to the y-axis

  5. Symmetry with respect to the origin (x, y)  (-x, -y) (2, 2)  (-2, -2) (1, -2)  (-1, 2) Odd Function

  6. Test for an Odd Function • A function y = f(x) is odd if , for each x in the domain of f. f(-x) = -f(x) Symmetry with respect to the Origin

  7. Tests for Even and Odd Functions • Even: f(-x) = f(x) • Odd: f(-x) = -f(x) • Both begin with f(-x)

  8. End Behavior • The end behavior of a function’s graph is the behavior of the graph as x approaches positive infinity (+∞) or negative infinity (-∞). • If the degree is odd and the leading coefficient is positive: f (x) → - ∞ as x → - ∞ and f (x) → +∞ as x → +∞ . • If the degree is odd and the leading coefficient is negative: f (x) → + ∞ as x → - ∞ and f (x) → - ∞ as x → +∞ . Right Left Down Left Right Up Up Left Down Right

  9. Up If the degree is odd and the leading coefficient is positive:f (x) → - ∞ as x → - ∞andf (x) → +∞ as x → +∞ . Left Right Down

  10. Up If the degree is odd and the leading coefficient is negative:f (x) → + ∞ as x → - ∞ andf (x) → - ∞ as x → ∞ . Left Right Down

  11. The following slides provide practice problems on this lesson. Use these examples to help you with your homework!

  12. Describe the end behavior of the graph of the function.

  13. Graph the function. Compare the graph with the graph of

  14. Tell whether the function is even, odd, or neither.

  15. Homework Assignment: Page 128 # 1 – 6, 10 – 15 allPage 129 # 1 – 3, 5 – 11 all

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