graphs & models (precalculus review 1) september 8th, 2015
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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.