CUBIC FUNCTIONS

PARENT FUNCTION

• Rule: f(x)=x^3
• Based on the equation, x is cubed

PARENT FUNCTION

• Table
• Based on the table, when x is a
• negative number the y is a negative
• number. When x is a positive number
• the y is a positive number.

PARENT FUNCTION

• Graph
• Based on the graph, it makes
• an "S" shaped line.

SYMBOLIC FUNCTION FORM

• f(x)=a(x-h)^3+k
• "a" represents if the line is reflected over the x axis.
• It will stretch or shrink the graph.
• Multiply the y values in the parent function by whatever
• "a" is to get the y values of the other equation.

SYMBOLIC FUNCTION FORM

• f(x)=a(x-h)^3+k
• "h" represents if the line is translated left or right on the graph.
• It shifts left or right on the x-axis.
• Add or subtract the x values of the parent function
• for whatever "h" is to get the x values of the other equation.

SYMBOLIC FUNCTION FORM

• f(x)=a(x-h)^3+k
• "k" represents if the line is shifted up or down on the graph.
• It moves up or down the y-axis.
• Add or subtract the y values of the parent function
• by whatever "k" is to get the y values of the other equation.

WRITING AN EQUATION FOR CUBIC FUNCTION TRANSFORMATION

• Add or subtract outside the original function f(x)=x^3
• f(x)=x^3+6 or f(x)=x^3-6
• Add or subtract inside the original function f(x)=x^3
• f(x)=(x+6)^3 or f(x)=(x-6)^3

CONTINUE OF WRITING AN EQUATION

• Multiply or divide the original function f(x)=x^3
• f(x)=6x^3 or f(x)=1/6x^3
• Negative in front of original function f(x)=x^3
• f(x)=--x^3

GRAPHING AN EQUATION FOR CUBIC FUNCTION TRANSFORMATION

• Add outside the original function f(x)=x^3
• f(x)=x^3+6 moves the line up the y-axis
• Subtract outside the original function f(x)=x^3
• f(x)=x^3-6 moves the line down the y-axis

CONTINUE OF GRAPHING AN EQUATION

• Add inside the original function f(x)=x^3
• f(x)=(x+6)^3 moves the line left on the x-axis
• Subtract inside the original function f(x)=x
• f(x)=(x-6)^3 moves the line right on the x-axis

CONTINUE OF GRAPHING AN EQUATION

• Multiply the original function f(x)=x^3
• f(x)=6x^3 shrinks the line
• Divide the original function f(x)=x^3
• f(x)=1/6x^3 stretches the line

CONTINUE OF GRAPHING AN EQUATION

• Negative in front of original function f(x)=x^3
• f(x)=--x^3 rotates the graph

FUNCTION QUESTIONS

• It is a function, because every x has 1 y
• D:all real #'s. R:all real #'s
• Increasing:(-oo,oo) Decreasing:never
• Positive:(0,oo) Negative:(-oo,0)

FUNCTION QUESTIONS

• As x--> oo, y--> oo
• As x--> -oo, y--> -oo
• No critical points
• X and Y intercepts (0,0)
• The inverse is a function, because every y has 1 x

THE END