Graphs & Models (Precalculus Review 1) September 8th, 2015.

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Presentation transcript:

Graphs & Models (Precalculus Review 1) September 8th, 2015

Ex. 1: Sketch the graph of each. A) B) C) D) E) I. Basic Graphs

II. Transformations of Functions Basic Transformations (c>0): Original Graph y=f(x) Horizontal shift c units right y=f(x-c) Horizontal shift c units left y=f(x+c) Vertical shift c units up y=f(x)+c Vertical shift c units down y=f(x)-c Reflection about the x-axis y=-f(x) Reflection about the y-axis y=f(-x) Reflection about the origin y=-f(-x)

Ex. 2: Find the x- and y-intercepts of the graph of y = x 3 - 5x 2 - 6x.

III. Intercepts of a Graph Def: The x-intercept of a graph is the point (a, 0) where the graph crosses the x-axis. Find it by plugging y = 0 into the equation and solving for x. The y-intercept is the point (0, b) where the graph crosses the y- axis. Find it by plugging x = 0 into the equation and solving for y.

Ex. 3: Use a graphing utility to find the x- and y- intercepts of the graph of y = x 4 - 3x 3 + 2x 2 - x - 4.

IV. The Domain & Range of a Function Def. The domain is the set of all input values for x. The range is the set of all outcomes of f(x).

Ex. 4: Find the domain and range of each function. a. f(x)=x 2 +2 b. c. h(t)=sec t d.