Absolute Value Function Do Now Roughly sketch the following different types of graphs. Don’t make them perfect! Do your best. Linear function Quadratic Function Cubic Function Square Root Function Cube Root Function Absolute Value Function

Appendix D Graphing Techniques Day 1 Objective: SWBAT review graphing techniques of stretching & shrinking, reflecting, symmetry and translations.

Parent Functions The most basic function within a function family that all other functions are based off of. The following slides represent the parent functions with their corresponding function families.

Identity Function Domain: all reals Range: all reals

Square Function (a quadratic formula) Domain: all reals Range: [0, ∞)

Cube Function Domain: all reals Range: all reals

Square Root Function Domain: [0, ∞) Range: [0, ∞)

Cube Root Function Domain: all reals Range: all reals

Absolute Value Function Domain: all reals Range: [0, ∞)

Vertical Shift The graph of y = f(x) + k can be obtained from the graph of y = f(x) by vertically translating (shifting) the graph of the latter upward k units if k is positive and downward |k| units if k is negative.

Graph y = |x| and y = |x| + 4. Describe the transformation from the parent function. Create a table of 5 points. Choose the middle point so that it makes the inside of the absolute value zero! This point is called your vertex. (This applies for absolute value and quadratic functions.)

Vertical Shift

Graph the following two functions: 𝒚= 𝒙 𝟐 and 𝒚= 𝒙 𝟐 −𝟓 Graph the following two functions: 𝒚= 𝒙 𝟐 and 𝒚= 𝒙 𝟐 −𝟓. Describe the transformation from the parent function.

Horizontal Shift The graph of y = f(x + h) can be obtained from the graph of y = f(x) by horizontally translating (shifting) the graph of the latter h units to the left if h is positive and |h| units to the right if h is negative.

Graph y= |x + 4|. Describe the transformation from y = |x|.

Graph y = |x - 5|. Describe the transformation from y = |x|.

Graph y = |x - 2|+3. Describe the transformation from y = |x|.

Describe the transformations for the following functions from their parent functions. 𝑓 𝑥 = 𝑥 2 +16 𝑔 𝑥 = 𝑥−9 2 −8 ℎ 𝑥 = 𝑥+2 −3 𝑓 𝑥 = 𝑥−3 +8

Write a NEW function g(x) based on the following transformations to the given function. 𝑓 𝑥 = 𝑥 2 --- translated 2 units right and 3 units down 𝑓 𝑥 = 𝑥+2 --- translated 2 units down and 1 units right 𝑓 𝑥 = 𝑥−3 2 −7--- translated 5 units up and 7 units left

Horizontal & Vertical Shifts If the shift happens outside the function, it is vertical. If the shift happens inside the function, it is horizontal.

Homework: Translations on Parent Functions Review Worksheet # 4, 6, 10, 13, 15, 16