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**1.4 – Shifting, Reflecting, and Stretching Graphs**

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**In this section, you will learn to:**

identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the equation of a transformed graph using the sketch of the graph

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Common Unit Graphs: 1) Constant Function:

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Common Unit Graphs: 2) Linear Function:

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Common Unit Graphs: 3) Absolute Value Function:

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Common Unit Graphs: 3) Absolute Value Function:

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Common Unit Graphs: 4) Quadratic Function:

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Common Unit Graphs: 4) Quadratic Function:

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Common Unit Graphs: 5) Square Root Function:

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Common Unit Graphs: 5) Square Root Function:

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Common Unit Graphs: 6) Cubic Function:

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Common Unit Graphs: 6) Cubic Function:

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Common Unit Graphs: 7) Rational Function:

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Common Unit Graphs: 7) Rational Function:

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**Summary of Graphing: Rigid Transformations: Shape/size do not change**

a) Vertical shift c units upward:

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**Summary of Graphing: Rigid Transformations:**

b) Vertical shift c units downward:

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**Summary of Graphing: Rigid Transformations:**

c) Horizontal shift c units to the right:

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**Summary of Graphing: Rigid Transformations:**

d) Horizontal shift c units to the left:

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**Summary of Graphing: Rigid Transformations:**

e) Reflection across the x-axis:

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**Summary of Graphing: Rigid Transformations:**

f) Reflection across the y-axis:

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**Summary of Graphing: Non-Rigid Transformations: Shape/size will change**

a) Vertical stretch by c units if c > 1 :

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**Summary of Graphing: Non-Rigid Transformations:**

b) Vertical shrink by c units if 0 < c < 1:

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**Graphing Examples: Describe the transformation of the following**

Function: This is an absolute value function shifted a) 4 units to the right b) 6 units up c) reflection across the x-axis d) vertical shrink

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Graphing Examples:

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**Y-Axis Reflection Graphing Examples:**

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**Graphing Examples: Write a cubic equation with the following**

transformations: a) 3 units to the left b) 2 units down c) reflection across the x-axis d) vertical stretch

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Graphing Examples:

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Writing an Equation: Write the equation of the graph below.

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Writing an Equation: Write the equation of the graph below.

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**Writing an Equation: 3 units right 2 units up x-axis reflection**

Write down the transformations. 3 units right 2 units up x-axis reflection Use (4,1) as a point on the graph

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Writing an Equation: Write the quadratic equation of the graph below.

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**Writing an Equation: The graph has been reflected across the x-axis.**

The vertex has been translated 1 unit to the right and 1 unit up. This represents (h,k). The graph has been reflected across the x-axis. Use one point on the graph, the vertex and solve for the value of a for the quadratic equation

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**Writing an Equation: One point on the graph is Solve for a.**

The vertex is (h,k) which is (1,1). One point on the graph is Solve for a.

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Writing an Equation: Sketch the graph of f(x+1) given the following function.

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Writing an Equation: Sketch the graph of f(x)-3 given the following function.

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Writing an Equation: Sketch the graph of f(-x) given the following function.

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Writing an Equation: Sketch the graph of - f(x)+1 given the following function.

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Writing an Equation: Sketch the graph of 2f(x)-1 given the following function.

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The following are what we call The Parent Functions.

The following are what we call The Parent Functions.

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