PreCalculus
Sec. 1.3
Graphs of Functions
The Vertical Line Test for Functions
• If any vertical line intersects a graph in more
than one point, the graph does not define y as
a function.
Ex1. Use the vertical line test to identify graphs in which
y is a function of x.
a.
b.
y
c.
y
x
d.
y
x
y
x
x
Obtaining Information from a Graph
• A closed dot: the graph stops at that point and the point
____________to the graph.
• An open circle: the graph stops at that point and the point
__________________________to the graph.
• An arrow: the graph extends to ___________ with the same
direction. (May not see with a graphing utility)
• f(a): the ________________(value) where x = a on the graph.
• Domain: all __________________from left to right.
• Range: all ____________________from bottom to top.
Use a graphing utility to graph the function and
find its domain and range. Then find f(0).
1)
f (x)  64  x
f (0) 
2
• Where does f(x) = 0: list the ____________________.
• Where is f(x) ≥ 0: state the _____________where the graph
____________________the x-axis.
• Increasing part: state the ______________where the graph
______________________. (excluding the endpoints)
•Decreasing part: state the _____________where the graph
______________________. (excluding the endpoints)
•Constant part: state the __________where the graph stays
a ____________________. (excluding the endpoints)
• Relative Maximum value: state the _____________of
the vertex on the curve that is
_____________________________________. Usually
expressed as an ordered pair: (x, y).
• Relative Minimum value: state the _____________of
the vertex on the curve that is ___________________.
Usually expressed as an ordered pair: (x, y).
• Relative Maxima or Minima: the relative
______________________________. in plural form.
1. Find f (0).
2. What is the value of f at x = 1?
What are the coordinates?
3. Where is f (x)  0 ?
State the x - values, interval notation.
4. Relative Maximum value :
5. Relative Minimum value :
6. Where is the graph increasing?
State the x - values, interval notation.
7. Where is the graph decreasing?
State the x - values, interval notation.
Use a graphing utility to graph the function and
determine the intervals on which the function is
increasing, decreasing, and constant.
f (x)   x  4  x 1
Increasing on:
Constant on:
Decreasing on:
You can use the trace key
and the left/right arrows if
necessary.
Use a graphing utility to graph the function and
approximate any relative minimum or maximum values
of the function.
h(x)  x  3x 10
3
2
Use the TRACE key for approximate.
For actual:
1. Use the 2nd key, followed by the
TRACE (CALC) key.
2. Choose 3: minimum or 4: maximum,
3. For Left bound, use the arrow to move
the “blinking X” just to the left of the
Minimum, ENTER.
4. Now repeat to the right for Right bound,
ENTER.
5. Guess? ENTER
Relative Minimum:
Relative Maximum:
Approximate:
Approximate:
Actual:
Actual:
Use the Graph to find the following:
Relative Minimum:
Decreasing:
Increasing: