

Introduction to Parent Graphs & Transformations #1
Presentation
•
Mathematics
•
9th Grade
•
Practice Problem
•
Easy
Standards-aligned
Trudy Hoss
Used 41+ times
FREE Resource
12 Slides • 20 Questions
1
Parent Graphs & Transformations #1

2
Parent Graph
A parent graph is the simplest graph for a family of functions.
3
Families of Graphs
You should be able to identify which family a graph belongs to by shape or equation.
4
The linear parent
y = x
The linear parent passes through
(0, 0) and has a slope of 1.
5
Multiple Choice
Which graph belongs to the linear family?
6
Multiple Choice
Which graph belongs to the linear family?
7
Linear Equations
All linear equations will have the form y = mx + b
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Multiple Choice
Which equation is a linear equation?
y=x2+1
y=∣x∣−2
y=2x+3
y=2x
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Multiple Choice
Which equation is a linear equation?
y=21x−4
y= 3x−2
y=x3+2
y=7x
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The Quadratic Parent y=x2
Quadratic graphs are a U shape. The parent graph passes through
(0, 0), then (1, 1), and (2, 4).
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Multiple Choice
Which graph belongs to the quadratic family?
12
Multiple Choice
Which graph belongs to the quadratic family?
13
Quadratic Equations
Quadratic equations will have an
x2 in the equation.14
Multiple Choice
Which equation is a quadratic equation?
y=x2+1
y=∣x∣−2
y=2x+3
y=2x
15
Multiple Choice
Which equation is a quadratic equation?
y=21x−4
y= 3x−2
y=x3+2
y=5x2+6
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The Cubic Parent y=x3
Also called the cube parent. This graph passes through (-1, -1), (0, 0), and (1, 1). Then it curves upward and downward.
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Multiple Choice
Which graph is a cubic graph?
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Multiple Choice
Which graph is a cubic graph?
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Cubic Equations
Cubic equations (or cube) will have an
x3 in the equation.20
Multiple Choice
Which equation is a cubic equation?
y=x2+1
y=∣x∣−2
y=4x3−1
y=2x
21
Multiple Choice
Which equation is a cubic equation?
y=21x−4
y= 3x−2
y=x3+2
y=5x2+6
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Absolute Value Parent y = |x|
The graph is a V shape and passes through (0, 0), (-1, 1) and (1, 1).
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Multiple Choice
Which graph belongs to the absolute value family?
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Multiple Choice
Which graph belongs to the absolute value family?
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Absolute Value Equations
The equations will always have x between vertical bars | x |
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Multiple Choice
Which equation is an absolute value equation?
y=x2+1
y=∣x∣−2
y=4x3−1
y=2x
27
Multiple Choice
Which equation is an absolute value equation?
y=21x−4
y= 3x−2
y=x3+2
y=∣5x+6∣
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Transformations
Shift- when the graph moves up, down, left, or right
Reflection- when the graph is "flipped" over the x or y-axis.
Vertical stretch or compression- the graph will look "skinnier" or "fatter"
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Multiple Choice
What transformation has occurred to the parent graph? The dashed graph is the parent.
The graph shifted down 4 units.
The graph shifted right 4 units.
The graph shifted up 4 units.
The graph shifted left 4 units.
30
Multiple Choice
What transformation has occurred to the parent graph? The dashed graph is the parent.
The graph shifted down 1 unit.
The graph shifted right 1 unit.
The graph shifted up 1 unit.
The graph shifted left 1 unit.
31
Multiple Choice
What transformation has occurred to the parent graph? The dashed graph is the parent.
The graph shifted down 1 unit.
The graph reflected over the x-axis.
The graph reflected over the y-axis.
32
Multiple Choice
What transformation has occurred to the parent graph? The green dashed graph is the parent and the blue solid graph is the transformed graph.
The graph shifted down 1 unit.
The graph reflected over the x-axis.
The graph reflected over the y-axis.
Parent Graphs & Transformations #1

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