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)+cVertical shift c units down y=f(x)-cReflection 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 = x3 - 5x2 - 6x.

III. Intercepts of a GraphDef: 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 = x4 - 3x3 + 2x2 - 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)=x2+2b. c. h(t)=sec t

d.