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Section 3.6

Section 3.6. Analysis of a Function. Objective : To be able to sketch the graph of a function based on an analytical approach. x-intercepts: set and find x-values. y-intercepts: find Symmetry: y-axis → origin → Continuity: intervals where

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Section 3.6

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  1. Section 3.6 Analysis of a Function

  2. Objective: To be able to sketch the graph of a function based on an analytical approach. • x-intercepts: set and find x-values. • y-intercepts: find • Symmetry: y-axis → origin → • Continuity: intervals where • Domain: all values of x that have functional values. • Range: switch x and y, resolve for y, then repeat #5.

  3. 7. Vertical Asymptotes: • Differentiability: all values of x where the derivative is defined. • Extrema: endpoints. • Concavity: • Points of Inflection: • Horizontal Asymptotes: • Period (of a trig function): normal periods are 2π for sin, cos, csc, sec and π for tan, and cot. It changes when a number is in front of the variable – divide period by #. • Slant Asymptote: when degree of numerator is one more than degree of denominator.

  4. Analyze and sketch the graph. 1. _ _ + + 2 -2 0 Rel min @ (0, 4.5) No rel max

  5. _ _ + 2 -2 No infl. pts b/c f(-2) and f(2) are undefined.

  6. Domain: (-∞, -2), (-2, 2), (2, ∞) Vertical Asymptote: x = 2, x = -2 Horizontal Asymptote: y = 2 Symmetry: y-axis symmetry x-intercepts: (-3, 0), (3, 0) y-intercept: (0, 4.5) Intervals: (-∞, -2) → decr, cd (-2, 0) → decr, cu (0, 2) → incr, cu (2, ∞) → incr, cd

  7. Analyze and sketch the graph. 2. _ No relative extrema

  8. _ + Infl. Pt. @

  9. Domain: Vertical Asymptote: Horizontal Asymptote: none Symmetry: none x-intercepts: y-intercept: (0, 1) Intervals: → decr, cu → decr, cd

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