Parent Graphs & Transformations

1. Parent Graphs & Transformations By Holly Carlson

2. Quadratic • y = x² • General shape: U • Domain: (-∞, ∞) • Formula: • Y= A*(x+B)² + C http://images.google.com/imgres?imgurl=http://people.richland.edu/james/lecture/m116/functions/quadratic.gif&imgrefurl=http://www.richland.edu/james/lecture/m116/functions/translations.html&usg=__Q6J3_Ivt0g4oZ0ni95ENG1jXLCo=&h=271&w=278&sz=4&hl=en&start=4&um=1&tbnid=BdlUN4wIxMgYLM:&tbnh=111&tbnw=114&prev=/images%3Fq%3Dquadratic%2Bfunction%26um%3D1%26hl%3Den Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

3. Linear & Geometric Transformations • Linear Transformations: • When B is positive, it shifts to the left “B” units • When B is negative, shifts to the right “B” units • When C is positive, it shifts up “C” units • When C is negative, it shifts down “C” units • Geometric Transformations: • If A is negative, the graph flips over the x-axis • When A is between 0-1 it gets wider (closer to the x-axis) • When A is greater than 1, it gets narrower (closer to the y-axis) Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

4. Quartic • y=x⁴ • General shape: U • Domain: (-∞,∞) • Formula: • y=A*(x+B)⁴+C • Apply linear/geometric transformations The quartic graph is shaped like the quadratic but is closer to the y-axis Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

5. Cubic • Y = x³ • General shape: S • Domain: (-∞, ∞) • Formula: • Y = A * (x+B)³ + C • Apply linear/geometric transformations http://images.google.com/imgres?imgurl=http://people.richland.edu/james/lecture/m116/functions/quadratic.gif&imgrefurl=http://www.richland.edu/james/lecture/m116/functions/translations.html&usg=__Q6J3_Ivt0g4oZ0ni95ENG1jXLCo=&h=271&w=278&sz=4&hl=en&start=4&um=1&tbnid=BdlUN4wIxMgYLM:&tbnh=111&tbnw=114&prev=/images%3Fq%3Dquadratic%2Bfunction%26um%3D1%26hl%3Den Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

6. Y = x⁵ • General shape: S • Domain: (-∞,∞) • Formula: • y = A * (x+B)⁵+ C • Apply linear/geometric transformations The y=x^5 graph is shaped like the cubic graph, but is closer to the y-axis Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker

7. Square Root • y=√x • General shape: • Domain: (0,∞) • Formula: y=A*(√x+B)+C • Apply linear/geometric transformations Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker http://www.epcc.edu/student/tutorial/Mathcenter/handouts/algebrahandouts/Parent%20graph%20of%20functions%20transf.pdf

8. Absolute Value • y= |x| • General shape: V • Domain: (-∞,∞) • Formula: • y=A*|x+B|+C • Apply linear/geometric transformations Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker http://www.epcc.edu/student/tutorial/Mathcenter/handouts/algebrahandouts/Parent%20graph%20of%20functions%20transf.pdf

9. Cube Root • y= ³√x • General shape: • Domain: (-∞,∞) • Formula: • A* (³√x+B) +C • Apply linear/geometric transformations Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker http://www.epcc.edu/student/tutorial/Mathcenter/handouts/algebrahandouts/Parent%20graph%20of%20functions%20transf.pdf

10. y=1/x • General shape: • Formula: • y=A*(1/x+B)+C • Apply linear/geometric transformations http://illuminations.nctm.org/java/whelk/Whelk-Graph1OverX.jpg Unit 2- Notes 1 “Parent Graphs & Transformations” By Miss Schmucker