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Lesson 3.1 Graph Cubic Functions. Goal Graph and analyze cubic functions. Vocabulary Page 126. 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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## Lesson 3.1 Graph Cubic Functions

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**Lesson 3.1Graph Cubic Functions**Goal Graph and analyze cubic functions.**Vocabulary Page 126**• A cubic function is 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 function if f (-x) =-f (x). • The graphs of odd functions are symmetric about the origin. • A function f is an even function if f (-x) = f (x). • The graphs of even functions are symmetric about the y-axis.**Even Function**Y – Axis SymmetryFold the y-axis (x, y) (-x, y) (x, y) (-x, y)**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**Symmetry with respect to the origin**(x, y) (-x, -y) (2, 2) (-2, -2) (1, -2) (-1, 2) Odd Function**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**Tests for Even and Odd Functions**• Even f(-x) = f(x) • Odd f(-x) = -f(x) • Both begin with f(-x)**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**Up**If the degree is odd and the leading coefficient is positive:f (x) → - ∞ as x → - ∞andf (x) → +∞ as x → +∞ . Left Right Down**Up**If the degree is odd and the leading coefficient is negative:f (x) → + ∞ as x → - ∞ andf (x) → - ∞ as x → -∞ . Left Right Down**Homework Lesson 3.1 Page 128 # 10 – 15 all**Lesson 3.1 Page 129 # 5-11

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