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

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Presentation transcript:

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

 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

 Y=(x-3)  (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  X 3 -9x2+27x-7 STANDARD FORM

 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

EXAMPLES OF TRANSLATIONS Reflection Stretch Compression HorizontalVertical

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

 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)

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) SOLO WORK TIME

 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

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