 Important things to remember:
Section 2.1
Slope of line: This equation calculates the slope of a line that connects two points.
𝑚=
𝑦2 − 𝑦1 𝑦 𝑐𝑜𝑜𝑟𝑖𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑜𝑖𝑛𝑡 − 𝑦 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑖𝑛𝑡
=
𝑥2 − 𝑥1 𝑥 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑡𝑎𝑡𝑒 𝑜𝑓 𝑠𝑒𝑐𝑜𝑛𝑑 𝑝𝑜𝑖𝑛𝑡 − 𝑥 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑖𝑛𝑡
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: 𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏 )
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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
(𝑥1 , 𝑦1 ) = 𝑎 𝑝𝑜𝑖𝑛𝑡 𝑜𝑛 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒
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
 f(x) = -1x2 will be the same as that of f(x) = x2,but it will be reflected over the xaxis

o
𝑓(𝑥) = −1√𝑥 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑎𝑡 𝑜𝑓 𝑓(𝑥) =
√𝑥, 𝑏𝑢𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑥 − 𝑎𝑥𝑖𝑠
Reflect over y –axis: To reflect a over the y-axis replace the x with (-x)
o For example the graph of

𝑓(𝑥) = √−𝑥 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑎𝑡 𝑜𝑓 𝑓(𝑥) =
√𝑥, 𝑏𝑢𝑡 𝑖𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑦 − 𝑎𝑥𝑖𝑠
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
 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

o
𝑓(𝑥) = √𝑥 − 5 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑜𝑓 𝑓(𝑥) =
√𝑥, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑖𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 5 𝑢𝑛𝑖𝑡𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡
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
 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

𝑓(𝑥) = √𝑥 + 5 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑜𝑓 𝑓(𝑥) =
√𝑥, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑖𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 5 𝑢𝑛𝑖𝑡𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡
o
Shifting a graph up: Add a number after the comparable function
o For example the graph of
 f(x) = x2 + 3 will be the same as the graph of f(x) = x2, except it will be shifted 3
units up
 𝑓(𝑥) = √𝑥 + 5 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑜𝑓 𝑓(𝑥) =
√𝑥, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑖𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 5 𝑢𝑛𝑖𝑡𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑢𝑝
o
Shifting a graph down: Subtract a number after the comparable function
o For example the graph of
 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
 𝑓(𝑥) = √𝑥 − 5 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ 𝑜𝑓 𝑓(𝑥) =
√𝑥, 𝑒𝑥𝑐𝑒𝑝𝑡 𝑖𝑡 𝑤𝑖𝑙𝑙 𝑏𝑒 𝑠ℎ𝑖𝑓𝑡𝑒𝑑 5 𝑢𝑛𝑖𝑡𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑑𝑜𝑤𝑛