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Section 2.7 – A Preview of Transformations. Objective: Identify the transformation(s) from one function to another Standard: 2.8.11.Q. Represent functional relationships in tables, charts, and graphs. Parent Functions. Quadratic Function f(x) = x 2 Absolute Value Function f(x) = lxl - PowerPoint PPT Presentation
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Section 2.7 – A Preview of Transformations
• Objective:– Identify the transformation(s) from
one function to another
• Standard:– 2.8.11.Q. Represent functional
relationships in tables, charts, and graphs
Parent Functions• Quadratic Function
f(x) = x2
• Absolute Value Function
f(x) = lxl
• Radical Function
f(x) = √x
Vertical Translations• Consider the Quadratic parent function
– How can we move this graph 2 spaces up?
– How about 4 spaces down?
Horizontal Translations • Consider the Absolute Value parent
function • How can we move this graph 3 spaces
to the left?
• How about 5 spaces to the right?
Vertical Stretch and Compression
• Consider the Radical parent function• How can we vertically stretch this graph
by a factor of 4?
How can we vertically compress this graph How can we vertically compress this graph by a factor of ½ ?by a factor of ½ ?
Horizontal Stretch and Compression
• Lets consider the Quadratic parent function.• How can we horizontally stretch this graph by a
factor of 4?
• How can we horizontally compress this graph by a factor of ⅓?
Reflections• Let’s consider the Radical parent function• How can we Vertically Reflect (across the x-
axis) this graph?
• How can we Horizontally Reflect (across the y-axis) this graph?
Combined Transformations
1. xxg 4)( Horizontal Reflection & Horizontal Compression by a factor of ¼
2. 34)( xxg Vertical Reflection, Horizontal Translation 4, & Vertical Translation 3
Identify each transformation from the parent function xxf )(
Write the function for each graph described.
3. The graph of vertically stretched by a factor of 2 and translated 1 unit to the right.
2)( xxf 2)1(2)( xxg
4. The graph of reflected across the x-axis, stretched horizontally by a factor of 5 and translated up 4
xxf )(
45
1)( xxh
Summary
Homework
Integrated Algebra II- Section 2.7 Level A
Honors Algebra II- Section 2.7 Level B