# Chapter 4 notes ```Algebra
Ch4 Functions
Review 4.1-3
New 4.4-6
Write this down:
• Function – a relationship between variables in
which each value of the input variable is
associated with a unique value of the output
variable.
• Can be shown as graphs, tables, equations, or
words, sets of ordered pairs.
Linear Functions
• Functions that can be defined by linear
equations
• Linear equations are first-degree equations –
no powers of 2 or greater.
• Slope-intercept form: y = mx + b
• Function notation: f(x) = mx + b
• Sample: when m = 2 and b = 3, f(x) = 2x + 3
Sample: when m = 2 and b = 3, f(x) = 2x + 3
f(x) = 2x + 3
(x, f(x))
f(0) = 2(0) + 3 = 0 + 3 = 3
(0, 3)
f(1) = 2(1) + 3 = 2 + 3 = 5
(1, 5)
For each x value, there is only one f(x) value.
Not a function: x = k because there is more than
one value.
If x = 3, then y can
be any + or – value.
A vertical line is not
a function!
• 4.1 We have already used graphs to relate 2
quantities. Page 252/8,9,10
• 4.2 Patterns &amp; Linear Functions.
– A dependent variable changes in response to
another variable, the independent variable.
– Input – independent variable
– Output – dependent variable
– 257/problem 2. As the number of photos
(independent variable) increases, the amount of
memory (dependent variable)decreases.
4.3 Patterns &amp; Nonlinear Functions
See page 262.
• Linear Function – its graph is a nonvertical line
or part of a nonvertical line
• Nonlinear Function – its graph is not a line or
part of a line
4.4: graphing of a function rule
Continuous graph –
unbroken
• Discrete graph – composed of distinct isolated
points
Page 270. Problem 1
Page 271, problem 2
Page 272, problem 3
Assignment: 274/9-21, 38-54evens
Day2, 4.4, page 273, prob. 4
• Graphing nonlinear function rules
• A. y = lXl – 4
• B. y = x2 + 1
273, problem 4 #4.
• Graph: y = x3 + 1
• Assignment: 275/23-31, 39-53odd
Nov. 29 Assignment:
283/8-14,16-18
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