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Transcript
A Review of Basic
Function Ideas
Lesson 2.1
Definitions
Function: No x’s repeat (it is okay if the y’s
repeat). On a graph, you can use the
Vertical line test – each vertical line can
only touch one point on the line)
Domain: x’s
Range: y’s
Discrete set: countable set (days of week)
Non-discrete set: Numbers between 1 and
2
Example 1
The volume V of a sphere is a function
of its radius r. Suppose V = g(r)
a. Find a formula that defines g
g = 4/3 ∏ r3
b. use the formula to estimate the
volume of Earth, if it has a radius of
6380 km.
V = 4/3 * ∏ 63803
V = 1,088,000,000,000 km3
Interval Notation
Interval
Graph
Closed
a
Interval
Notation
Set
Notation
[a,b]
{x: a≤ x ≤ b}
(a,b)
{x: a < x < b}
[b, ∞)
{x: x≤ b}
(∞, a)
{x: x< a}
b
Open
a
b
Closed infinite
interval
b
Open infinite
interval
a
Vertical Line Test
*If you draw a vertical line through the
graph of a function, it will intersect the
graph at no more than one point.
Example 2
Use interval notation to describe the
domain of the real function t with rule
Bottom: (2x - 3)(2x Union
- 3) so x ≠ 3/2
Domain: (-∞, 3/2) U (3/2, ∞)
Example 3
Describe the set in interval notation:
The set of points on the number line that
are at least 3 units away from the point
-1.
(-∞, -4] U [2, ∞)
Homework
Page 84
2 – 20
(evens)
