Unit 2: Transformations of functions Final Exam Review

Topics to cover Transformations of Functions Characteristic Points Factoring Simplifying Radicals

Transformations of functions You can move a function anywhere on a graph using transformations You can go: UP AND DOWN LEFT AND RIGHT STRETCH AND SHRINK REFLECT OVER THE X AXIS AND Y AXIS

Transformations UP AND DOWN Use these rules when translating a function up and down Up: f(x) + c Example: y = f(x) + 4 will move a function Up 4 Down: f(x) – c Example: y = f(x) – 5 will move a function Down 5

Transformations left and right Use these rules when translating a function left and right Left: f(x + c) Example: y = f(x + 2) will move a function Left 4 Right: f(x – c) Example: y = f(x – 6) will move a function Right 6

Stretch and Shrink Use these rules when stretching and shrinking c ∙ f(x) when c > 1 Example: y = 3 f(x) will stretch a function by 3 Shrink: c ∙ f(x) when 0 < c < 1 Example: y = 𝟐 𝟑 f(x) will shrink a function by 𝟐 𝟑

Reflections over the x axis and y axis Use these rules when reflecting a functions over the x axis or the y axis X axis: -f(x) The negative is OUTSIDE of the function Y axis: f(-x) The negative is INSIDE of the parenthesis with the x

Given the function, write the transformations Example y = 5 f(x – 3) y = -f(x) + 2 y = 1 3 f(−x+7) - 8 Answers Stretch 5, Right 3 Reflect over the X axis, Up 2 Shrink 𝟏 𝟑 , Reflect over the y axis, Left 7, Down 8

Given the function, write the transformations Now you try: y = f(x – 4) – 3 y = 6 f(x + 2) y = − 1 3 f(x) + 6

Given the transformations, write the equation Example Left 1, Up 9 Shrink 3 4 , Reflect over the x axis Stretch 10, Right 4, Down 2 Answers y = f(x + 1) + 9 y = - 𝟑 𝟒 f(x) y = 10 f(x – 4) – 2

Given the transformations, write the equation Now you try: Right 7, Reflect over the y axis Stretch 4, Left 2, Down 5 Reflect over the x axis, Shrink 4 5 , Up 8

CHARACTERISTIC points When transforming points, you must figure out: If the transformation is affecting the X VALUE or the Y VALUE Then ADD, SUBTRACT, or MULTIPLY the point by the correct value UP AND DOWN will affect the y value LEFT AND RIGHT will affect the x value STRETCHING AND SHRINKING will affect the y value

CHARACTERISTIC points Example Move the point (5, -2) using the transformations in the function y = f(x – 4) Answer: (9, -2) *This transformation moves the function right 4, so the x value is moved right 4 spaces

CHARACTERISTIC points Now you try: Move the point (-4, 2) using the functions: y = f(x) – 5 y = f(x + 1) y = 3 f(x) y = f(x – 2) + 9

FACTORING Factoring helps you to find where a function crosses the X AXIS Steps to follow when factoring Draw an X For the number on the top of the X, MULTIPLY the FIRST number by the LAST number For the number on the bottom of the X, write the MIDDLE number Figure out which 2 numbers will MULTIPLY to get the top number on the X and ADD to get the bottom number on the X and use reverse Xbox method, or: SPLIT THE MIDDLE by rewriting your equation with the 2 numbers that you found on the X. Group the FIRST 2 TERMS and the LAST 2 TERMS. Take out the GCF of the first 2 terms and the last 2 terms Use your GCF and what was left over to write your equation in factored form

FACTORING Watch this Video for an example

FACTORING Try this one now: Factor 6x2 – 13x + 2

Simplifying Radicals Simplifying Radicals is necessary in math in order to simplify your answer COMPLETELY Steps to Follow: Break down the number under the radical using a FACTOR TREE CIRCLE any pairs of numbers The numbers that have a PAIR can be taken out of the radical and put on the OUTSIDE If there is more than one pair, MULTIPLY the numbers on the outside of the radical Write what is left over without a pair UNDER the radical symbol

Simplifying Radicals Now try this one: 135

ALL DONE