Name___________________________
Algebra 8 Unit 2 – Lesson 9 Notes
Functions and Restricted Domain
Recall a function is a rule which operates on an input (domain) and produces a single output.
Set Builder Notation and Discrete Graphs

set-builder notation - {function rule | type and constraints of the domain}

Discrete Graphs - are made of distinct, no connected points. The domain is usually whole numbers or
integers.
Example
Generate the ordered pairs and plot the graph of: {(𝑥, 2𝑥 + 1) | 𝑥 integer and 2 ≤ 𝑥 ≤ 7}
Domain
Range
Set Builder Notation and Continuous Graphs

Continuous Graphs - A Continuous graph is when all points are connected because there can be values in
between the integers.
Example
Generate the ordered pairs and plot the graph of: {(𝑥, 𝑥 2 + 1) | 𝑥 real, −2 ≤ 𝑥 ≤ 3}.
Domain
Range
Interval Notation D: ______________
Interval Notation R: ______________
Examples Use the vertical line test to determine whether each relation is a function.
a. {(3, 7), (1, 8), (3, -2), (5, 4), (6, 1)}
b.
Is it a function? ________________________
Is it a function? ___________________
What is the domain? ____________________
What is the domain in interval notation?
What is the range? ______________________
What is the range in interval notation?
c. The graph of 𝑥 = 2
d.
Is it a function? ________________________
Is it a function? ________________________
What is the domain? ____________________
What is the domain?
What is the range? ______________________
What is the range?
Increasing/Decreasing and Rel Max/Min
Review: Write the solution set to the following number lines in interval notation:
a)
b)
Function Vocabulary:
Increasing: A function is increasing if, as the x-values increase from left to right, the y-values
increase. (Use interval notation to describe the x-values where this happens.)
Decreasing: A function is decreasing if, as the x-values increase from left to right, the y-values
decrease. (Use interval notation to describe the x-values where this happens.)
Relative Maximum: A point where a function changes from increasing to decreasing (a peak)
Relative Minimum: A point where a function changes from decreasing to increasing (a valley)
Example 1:
Below is the graph of a quadratic function. Describe the intervals where the function is
increasing/decreasing. State whether the quadratic has a relative maximum or a relative minimum.
Example 2:
Below is an example of a polynomial function.
a) Which points (A, B, C, or D) are relative maximums?
b) Which points (A, B, C, or D) are relative
minimums?
c) Name the interval(s) where the function is
increasing.
d) Name the interval(s) where the function is
decreasing.
Example 3:
Below is an example of a piece-wise function.
a) Label any relative maximum with an A.
b) Label any relative minimum with a B.
c) Name the interval(s) where the function is
increasing.
d) Name the interval(s) where the function is
decreasing.
e) How do you know that this is a function?
f) State the domain.
g) State the range.