```Important things to remember:
Section 2.1
Slope of line: This equation calculates the slope of a line that connects two points.
๐=
๐ฆ2 − ๐ฆ1 ๐ฆ ๐๐๐๐๐๐๐๐๐๐ก๐ ๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐๐ก − ๐ฆ ๐๐๐๐๐๐๐๐๐ก๐ ๐๐ ๐๐๐๐ ๐ก ๐๐๐๐๐ก
=
๐ฅ2 − ๐ฅ1 ๐ฅ ๐๐๐๐๐๐๐๐ก๐๐ก๐ ๐๐ ๐ ๐๐๐๐๐ ๐๐๐๐๐ก − ๐ฅ ๐๐๐๐๐๐๐๐๐ก๐ ๐๐ ๐๐๐๐ ๐ก ๐๐๐๐๐ก
Vertical Lines:
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Vertical lines have a slope that is undefined
All points on a vertical line have the same x-coordinate
The equation of any vertical line contains an x, but not a y (x = 5, is an example)
Vertical lines have x-intercepts and do not have y-intercepts
Horizontal Lines:
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Horizontal lines have a slope that is 0
All points on a horizontal line have the same y-coordinate
The equation of any horizontal line contains a y, but not an x (y = 3, is an example)
Horizontal lines have y-intercepts and do not have x-intercepts
Slope Intercept form of an equation of a line: y = mx + b
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This equation allows you to find the slope of a line and the y-intercept without algebra
m = slope of the line
b = y-coordinate of the y-intercept
Point Slope form of an equation of a line: ๐ − ๐๐ = ๐(๐ − ๐๐ )
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This equation allows you to find a point on a line and the slope of a line without algebra
m = slope of the line
(๐ฅ1 , ๐ฆ1 ) = ๐ ๐๐๐๐๐ก ๐๐ ๐กโ๐ ๐๐๐๐
Parallel lines have equal slopes
Perpendicular lines have slopes that are negative reciprocals (that is the slopes are reciprocals with
opposite signs
Section 2.2 &amp; 2.3
Relation: A relation is a set of ordered pairs. (points)
Function: A function is a relation in which each x is unique.
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We say a relation is a function from A to B, provided:
o The x-coordinate of each point is from set A
o The y-coordinate of each point is from set B
o All of the x-coordinates are different
o It is okay if there is duplication of the y-coordinates
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We say a graph of a relation is a function , ( or more precisely if the graph of an equation
represents y as a function of x provided:
o The graph passes the vertical line test, that is no vertical line can be drawn to touch the
graph in more than one place
Section 2.5: Reflecting, shifting and stretching graphs
o
Reflect over x –axis: To flip over a graph we Multiply a function by (-1)
o For example the graph of
๏ง f(x) = -1x2 will be the same as that of f(x) = x2,but it will be reflected over the xaxis
๏ง
o
๐(๐ฅ) = −1√๐ฅ ๐ค๐๐๐ ๐๐ ๐กโ๐ ๐ ๐๐๐ ๐๐  ๐กโ๐๐ก ๐๐ ๐(๐ฅ) =
√๐ฅ, ๐๐ข๐ก ๐ค๐๐๐ ๐๐ ๐๐๐๐๐๐๐ก๐๐ ๐๐ฃ๐๐ ๐กโ๐ ๐ฅ − ๐๐ฅ๐๐
Reflect over y –axis: To reflect a over the y-axis replace the x with (-x)
o For example the graph of
๏ง
๐(๐ฅ) = √−๐ฅ ๐ค๐๐๐ ๐๐ ๐กโ๐ ๐ ๐๐๐ ๐๐  ๐กโ๐๐ก ๐๐ ๐(๐ฅ) =
√๐ฅ, ๐๐ข๐ก ๐๐ก ๐ค๐๐๐ ๐๐ ๐๐๐๐๐๐๐ก๐๐ ๐๐ฃ๐๐ ๐กโ๐ ๐ฆ − ๐๐ฅ๐๐
o
Shifting a graph to the right: Replace the x with x-# (inside a parenthesis, or under a square
root symbol)
o For example the graph of
๏ง f(x) = (x-3)2 will be the same as the graph of f(x) = x2, except it will be shifted 3
units to the right
๏ง
o
๐(๐ฅ) = √๐ฅ − 5 ๐ค๐๐๐ ๐๐ ๐กโ๐ ๐ ๐๐๐ ๐๐  ๐กโ๐ ๐๐๐๐โ ๐๐ ๐(๐ฅ) =
√๐ฅ, ๐๐ฅ๐๐๐๐ก ๐๐ก ๐ค๐๐๐ ๐๐ ๐ โ๐๐๐ก๐๐ 5 ๐ข๐๐๐ก๐  ๐ก๐ ๐กโ๐ ๐๐๐โ๐ก
Shifting a graph to the left: Replace the x with x+# (inside a parenthesis, or under a square
root symbol)
o For example the graph of
๏ง f(x) = (x+3)2 will be the same as the graph of f(x) = x2, except it will be shifted 3
units to the left
๏ง
๐(๐ฅ) = √๐ฅ + 5 ๐ค๐๐๐ ๐๐ ๐กโ๐ ๐ ๐๐๐ ๐๐  ๐กโ๐ ๐๐๐๐โ ๐๐ ๐(๐ฅ) =
√๐ฅ, ๐๐ฅ๐๐๐๐ก ๐๐ก ๐ค๐๐๐ ๐๐ ๐ โ๐๐๐ก๐๐ 5 ๐ข๐๐๐ก๐  ๐ก๐ ๐กโ๐ ๐๐๐๐ก
o
Shifting a graph up: Add a number after the comparable function
o For example the graph of
๏ง f(x) = x2 + 3 will be the same as the graph of f(x) = x2, except it will be shifted 3
units up
๏ง ๐(๐ฅ) = √๐ฅ + 5 ๐ค๐๐๐ ๐๐ ๐กโ๐ ๐ ๐๐๐ ๐๐  ๐กโ๐ ๐๐๐๐โ ๐๐ ๐(๐ฅ) =
√๐ฅ, ๐๐ฅ๐๐๐๐ก ๐๐ก ๐ค๐๐๐ ๐๐ ๐ โ๐๐๐ก๐๐ 5 ๐ข๐๐๐ก๐  ๐ก๐ ๐กโ๐ ๐ข๐
o
Shifting a graph down: Subtract a number after the comparable function
o For example the graph of
๏ง f(x) = x2 - 3 will be the same as the graph of f(x) = x2, except it will be shifted 3
units to the down
๏ง ๐(๐ฅ) = √๐ฅ − 5 ๐ค๐๐๐ ๐๐ ๐กโ๐ ๐ ๐๐๐ ๐๐  ๐กโ๐ ๐๐๐๐โ ๐๐ ๐(๐ฅ) =
√๐ฅ, ๐๐ฅ๐๐๐๐ก ๐๐ก ๐ค๐๐๐ ๐๐ ๐ โ๐๐๐ก๐๐ 5 ๐ข๐๐๐ก๐  ๐ก๐ ๐กโ๐ ๐๐๐ค๐
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