1. By: Natalie Cullinan, Kaylee Batchelor, Isabella Smith CUBIC FUNCTIONS

2.  Cubic functions are non-linear functions that can be written in the standard form: y=ax 3 +bx 2 +cx+d  The parent function is f(x)=x 3 CUBIC FUNCTION

3.  Y=(x-3) 3 +20  (x-3)(x-3)(x-3)+20  X 2 -3x-3x+9  (x 2 -6x+9)(x-3)+20  X 3 -3x2-6x 2 +18x+9x-27+20  X 3 -9x2+27x-7 STANDARD FORM

4.  Reflection: The function is flipped  Stretch/Compression: When the function is pulled out or pushed in  Horizontal: Left or Right  Vertical: Up or Down TRANSLATIONS

5. EXAMPLES OF TRANSLATIONS Reflection Stretch Compression HorizontalVertical

6.  Domain: Input values of a function  Range: Output values of a function Ex 1: x 3 +5 Domain=(-∞,∞) Range=(-∞,∞) DOMAIN AND RANGE

7.  Intercepts: when 2 functions touch each other on the graph INTERCEPT Find the intersection. Functions: y=x 3 +3 y=3x 3 +6 Answer: (-1.1,1.5)

8. 1.Standard form: f(x)= (x+5) 3 2.Domain and Range: f(x)=x3-4 3.Intercept: g(x)=-x 3 +3x 2 -1 f(x)=x 3 4.Translation: g(x)= (x+1) 3 - 3 SOLO WORK TIME

9.  Directions: in this activity you will practice on your cubic translations, intercepts, and domain and range. You will do the problems and then if you get it wrong, Mr. Pumpkin Man gains a body part! ACTIVITY: MONSTER MATH

10. 1.Describe the transformation(s). Given the parent function: f(x) = x 3 g(x)=x 3 +13 2. Describe the transformation(s). Given the parent function: (f)x = x 3 g(x)=-1/2(x+3) 3 -8 3. Find the Domain and Range g(x)= -x 3 -14 4. Find the intercepts. Given the parent function: f(x) = x 3 g(x)= (x+4) 3 HOMEWORK