 # 1.4 – Shifting, Reflecting, and Stretching Graphs

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1.4 – Shifting, Reflecting, and Stretching Graphs

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

Common Unit Graphs: 1) Constant Function:

Common Unit Graphs: 2) Linear Function:

Common Unit Graphs: 3) Absolute Value Function:

Common Unit Graphs: 3) Absolute Value Function:

Common Unit Graphs: 4) Quadratic Function:

Common Unit Graphs: 4) Quadratic Function:

Common Unit Graphs: 5) Square Root Function:

Common Unit Graphs: 5) Square Root Function:

Common Unit Graphs: 6) Cubic Function:

Common Unit Graphs: 6) Cubic Function:

Common Unit Graphs: 7) Rational Function:

Common Unit Graphs: 7) Rational Function:

Summary of Graphing: Rigid Transformations: Shape/size do not change
a) Vertical shift c units upward:

Summary of Graphing: Rigid Transformations:
b) Vertical shift c units downward:

Summary of Graphing: Rigid Transformations:
c) Horizontal shift c units to the right:

Summary of Graphing: Rigid Transformations:
d) Horizontal shift c units to the left:

Summary of Graphing: Rigid Transformations:
e) Reflection across the x-axis:

Summary of Graphing: Rigid Transformations:
f) Reflection across the y-axis:

Summary of Graphing: Non-Rigid Transformations: Shape/size will change
a) Vertical stretch by c units if c > 1 :

Summary of Graphing: Non-Rigid Transformations:
b) Vertical shrink by c units if 0 < c < 1:

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

Graphing Examples:

Y-Axis Reflection Graphing Examples:

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

Graphing Examples:

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

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

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

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

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

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.

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

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

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

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

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