Cubic Functions
http://jwilson.coe.uga.edu/emt668/emt668.folders.f97/wynne/cubic/cubic%20functions.html
Standard Form
f(x) = ax3 + bx2 + cx + d
Factored Form
f(x) = a(x - r1)(x - r2)(x - r3)
where r1, r2 and r3 are the roots.
http://www.mathopenref.com/cubicexplorer.html
How to translate
Phelps
Transformations
replace x
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flip over x
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flip over y
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stretch or shrink
stretch
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1. Graph the parent function y = x3 on your calculator.
2. Graph: y = x3 + 2
Compare your new graph to the parent graph. How does it change?
What is the y-intercept?
3. Graph: y = x3 - 2
Compare your new graph to the parent graph. How does it change?
What is the y-intercept?
4. Write the equation of a cubic function with a y-intercept of -3.
5. Write the equation of a cubic function with a y-intercept of 7.
1. Graph the parent function y = x3 on your calculator.
2. y = -x3
Compare your new graph to the parent graph. How does it change?
3
3. y = 0.5x
Compare your new graph to the parent graph. How does it change?
4. y = 4x3
Compare your new graph to the parent graph. How does it change?
Create a table for y = x3.
Graph the function.
Identify the domain: ______________
Identify the range: _______________
Does your graph have a maximum or minimum? ___________
Identify the intervals the function is increasing. _____________
Identify the intervals the function is decreasing. ____________
Describe the end behavior of your graph. _________________
What are the zeros of your function? _____________________
What is the x-intercept of your function? __________________
What is the y-intercept of your function? __________________
3
Create a table for y = x + 4.
Graph the function.
Identify the domain: ______________
Identify the range: _______________
Does your graph have a maximum or minimum? ___________
Identify the intervals the function is increasing. _____________
Identify the intervals the function is decreasing. ____________
Describe the end behavior of your graph. _________________
What are the zeros of your function? _____________________
What is the x-intercept of your function? __________________
What is the y-intercept of your function? __________________
Create a table for y = (x-1)3.
Graph the function.
Identify the domain: ______________
Identify the range: _______________
Does your graph have a maximum or minimum? ___________
Identify the intervals the function is increasing. _____________
Identify the intervals the function is decreasing. ____________
Describe the end behavior of your graph. _________________
What are the zeros of your function? _____________________
What is the x-intercept of your function? __________________
What is the y-intercept of your function? __________________
Create a table for y = 2x3.
Graph the function.
Identify the domain: ______________
Identify the range: _______________
Does your graph have a maximum or minimum? ___________
Identify the intervals the function is increasing. _____________
Identify the intervals the function is decreasing. ____________
Describe the end behavior of your graph. _________________
What are the zeros of your function? _____________________
What is the x-intercept of your function? __________________
What is the y-intercept of your function? __________________
Create a table for y = 4(x + 2)3 - 5.
Graph the function.
Identify the domain: ______________
Identify the range: _______________
Does your graph have a maximum or minimum? ___________
Identify the intervals the function is increasing. _____________
Identify the intervals the function is decreasing. ____________
Describe the end behavior of your graph. _________________
What are the zeros of your function? _____________________
What is the x-intercept of your function? __________________
What is the y-intercept of your function? __________________
Given graph write equation
Given graph write equation
Given graph write equation
Given graph write equation
Assignment:
Create a table for y = 3(x - 8)3 + 7.
Graph the function.
Identify the domain: ______________
Identify the range: _______________
Does your graph have a maximum or minimum? ___________
Identify the intervals the function is increasing. _____________
Identify the intervals the function is decreasing. ____________
Describe the end behavior of your graph. _________________
What are the zeros of your function? _____________________
What is the x-intercept of your function? __________________
What is the y-intercept of your function? __________________