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