Graphs of Functions
section 1.3
problem #1 - Using the graph below, find:
a. the domain
b. the range
c. the function values f(-1) and f(2).
(2,4)
(4,0)
(-1,-5)
problem #2 - Find the domain and range of f(x) =
x-4
.
Vertical Line Test for Functions
A graph is a function if and only if no vertical line intersects
the graph at more than one point.
problem #3 - Which of these graphs represent y as a function
of x?
(c)
(b)
(a)
Increasing, Decreasing, & Constant Functions
A function is increasing on an interval
if
.
A function is decreasing on an interval
if
.
A function is constant on an interval
.
if
problem #4 - For each graph below, determine the open intervals on
which the graph is increasing, decreasing, or constant.
(b)
(a)
(c)
* Continued on next page. *
section 1.3 (continued)
relative minimum - a minimum value of a function within a given
open interval
relative maximum - a maximum value of a function within a given
open interval
problem #5 - During a 24-hour period, the temperature y (in degrees
Fahrenheit) of a certain city can be approximated by the
model y = .026x 3- 1.03x 2 + 10.2x + 34, 0 x 24
where x represents the time of day, with x = 0
corresponding to 6 A.M. Approximate the maximum and
minimum temperatures during this 24-hour period.
greatest integer function
(step function)
- is the greatest integer that is less than
or equal to x
4
3
2
1
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6
-2
-3
-4
Question: What are the domain and range of the greatest integer
function ?
* Some real-life applications of a step function are postage and
telephone rates.
piecewise function - a function whose values are defined
differently within different domain intervals
problem #6 - Sketch the graph of the following piece-wise
function, both by hand and by graphing utility.
even function - has a graph symmetric with respect to the y-axis
A function f is even if f(-x) = f(x) for each x in its domain.
odd function - has a graph symmetric with respect to the origin
A function f is odd if f(-x) = - f(x) for each x in its domain.
problem #7 - Determine whether each function is even, odd, or neither.
a) f(x) = x
d) k(x) = x 3 - 1
b) g(x) = x 3 - x
c) h(x) = x 2 + 1