advertisement

Graphs & Models (Precalculus Review 1) September 8th, 2015 I. Basic Graphs Ex. 1: Sketch the graph of each. A) f (x) = (x -1) + 3 B) g(x) = x + 2 -1 C) h(x) = (x + 4) + 2 D) y(x) = - ln x E) 4 f (x) = x-6 2 3 II. Transformations of Functions Basic Transformations (c>0): Original Graph Horizontal shift c units right Horizontal shift c units left Vertical shift c units up Vertical shift c units down Reflection about the x-axis Reflection about the y-axis Reflection about the origin y=f(x) y=f(x-c) y=f(x+c) y=f(x)+c y=f(x)-c y=-f(x) y=f(-x) y=-f(-x) Ex. 2: Find the x- and y-intercepts of the graph of 3 2 y = x - 5x - 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 yaxis. Find it by plugging x = 0 into the equation and solving for y. Ex. 3: Use a graphing utility to find the x- and y4 3 2 intercepts of the graph of y = x - 3x + 2x - 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. 2 a. f(x)=x +2 b. g(x) = 4x +1 c. h(t)=sec t 1 d. f (x) = 3x -1