y sec x

1
y sec x

• Recall from the unit circle that
• sec r/x.
• sec is undefined whenever x 0.
• Between 0 and 2?, y sec x is undefined at x
  ?/2 and x 3?/2.

2
Domain

• Since sec x is undefined at ?/2, 3?/2, etc., the
  asymptotes appear at ?/2 k?

3
Range of Secant Function

• The range of every secant graph varies depending
  on vertical shifts.
• The range of the parent graph is
• (-?, -1U1, ?)

4
Period

• One complete cycle occurs between 0 and 2?.
• The period is 2?.

5
Critical Points

• The parent graph has a local maximum at (?, -1).
• The parent graph has a local minimum at
• (0, 1) and (2?,1).

6
y a sec b(x-c) d

• a vertical stretch or shrink
• If a gt 1, the graph has a vertical stretch .
• If 0ltalt1, the graph has a vertical shrink .
• If a is negative, the graph reflects about the
  x-axis.

7
y a sec b (x - c) d

• b horizontal stretch or shrink
• Period 2?/b
• If b gt1, the graph contains a horizontal shrink
  .
• If 0ltblt1, the graph contains a horizontal
  stretch.

8
y a sec b(x - c ) d

• c horizontal shift
• if c is negative, the graph shifts left c units.
• if c is positive, the graph shifts right c units.

9
y a sec b(x - c) d

• d vertical shift
• If d is positive, the graph shifts up d units.
• If d is negative, the graph shifts down d units

10
Parent Function y sec x

• Important Points
• asymptote
• Important Points
• asymptote
• Important Points
• asymptote

11
Graph y sec x
12
Graph y 3 sec x
13
Graph y sec ½ x
14
Graph
15
Graph y sec x - 3
16
Graph