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Questions/
Main Ideas:
Algebra 1
Notes
Name: ________________________
Period: _______Date: ___________
TOPIC: Introduction to Graphing Functions
OBJECTIVE: To recognize the 3 function forms and identify slope.
Functions are equations that describe how the “ x ” and “ y ” variables work together.
THREE FUNCTION FORMS
There are three important formats in which functions can be presented.
For example, below is the exact same function, presented in three different forms:
y  2x  7
slope-intercept
form
y  1  2  x  3
2x  y   7
point-slope
form
standard
form
SLOPE of a line
The slope of a graphed line is what says how inclined the line is.
A positive slope means
the right side of the line
points UP.
A negative slope means
the right side of the line
points DOWN.
A horizontal line
has a slope of zero.
A vertical line has
an undefined slope.
(line leans against
the floor)
(line does not lean
against anything)
Parallel lines
Perpendicular lines
(lines that lean the
same way) have
the same slope.
(lines that form a cross)
have negative reciprocal
slopes.
What is a NEGATIVE RECIPROCAL?

”Flip” the fraction upside down,

Then change the sign of the fraction.
Examples:
1) Find the negative reciprocal of the following numbers:
2
3
reciprocal:

________
1
5
________
7
9
3
8

________
________
________
1
_______
2) Circle the pairs that are negative reciprocals:
2 and 
1
2
5
2
and
2
5
1
and 3
3

1
and 6
6
10
13
and 
13
10
SLOPE of a function in function form
The slope of a function form equation IS the coefficient of the “ x ”.
Examples:
3) What is the slope of each functions below?
y
y  3x  1
slope: ______
2
x6
5
slope:_______
y  17  3 x
slope: _______
y
1
x 6
2
slope: ________
Parallel and Perpendicular functions in function form
Parallel lines have the same “ x ” coefficient (same number with an “ x ”)
Perpendicular lines have negative reciprocal “ x ” coefficient .
Examples:
Write a function that is parallel and another that is perpendicular.
y  3x  1
Summary:
y
2
x6
5
y  17  3 x
y
1
x 6
2
parallel:
parallel:
parallel:
parallel:
_______________
_________________
_________________
________________
perpendicular:
perpendicular:
perpendicular:
perpendicular:
_______________
_________________
_________________
________________