PRECALCULUS UNIT 1 NOTES
Functions & Their Graphs
What is a Function?
A function is a rule that matches each input (x-value) with exactly one output (y-value).
Function notation:
f(x) = 2x + 3
Example:
f(4) = 2(4) + 3 = 11
Vocabulary:
• Input = independent variable = x
• Output = dependent variable = y
• Domain = all possible x-values
• Range = all possible y-values
DOMAIN
The domain is the set of all x-values that can be used.
Restrictions:
1. Cannot divide by 0
2. Cannot have a negative number under an even root
Example:
f(x) = 3/(x - 5)
Domain:
x≠5
Example:
f(x) = √(x + 4)
Need:
x+4≥0
Domain:
x ≥ -4
EVALUATING FUNCTIONS
, Plug in the given value for x.
Example:
f(x) = x² - 3x + 2
Find f(5):
f(5) = (5)² - 3(5) + 2
= 25 - 15 + 2
= 12
Answer:
f(5) = 12
GRAPHS OF FUNCTIONS
Vertical Line Test
A graph represents a function if no vertical line hits it more than once.
If a vertical line touches the graph twice, it is NOT a function.
INTERCEPTS
x-intercept:
When y = 0
Example:
y=x-4
0=x-4
x=4
x-intercept = (4, 0)
y-intercept:
When x = 0
Example:
y=x-4
y = -4
y-intercept = (0, -4)
Functions & Their Graphs
What is a Function?
A function is a rule that matches each input (x-value) with exactly one output (y-value).
Function notation:
f(x) = 2x + 3
Example:
f(4) = 2(4) + 3 = 11
Vocabulary:
• Input = independent variable = x
• Output = dependent variable = y
• Domain = all possible x-values
• Range = all possible y-values
DOMAIN
The domain is the set of all x-values that can be used.
Restrictions:
1. Cannot divide by 0
2. Cannot have a negative number under an even root
Example:
f(x) = 3/(x - 5)
Domain:
x≠5
Example:
f(x) = √(x + 4)
Need:
x+4≥0
Domain:
x ≥ -4
EVALUATING FUNCTIONS
, Plug in the given value for x.
Example:
f(x) = x² - 3x + 2
Find f(5):
f(5) = (5)² - 3(5) + 2
= 25 - 15 + 2
= 12
Answer:
f(5) = 12
GRAPHS OF FUNCTIONS
Vertical Line Test
A graph represents a function if no vertical line hits it more than once.
If a vertical line touches the graph twice, it is NOT a function.
INTERCEPTS
x-intercept:
When y = 0
Example:
y=x-4
0=x-4
x=4
x-intercept = (4, 0)
y-intercept:
When x = 0
Example:
y=x-4
y = -4
y-intercept = (0, -4)
