AIgo NotesFlashcards for:
How to Graph Cubic Functions Using Transformations
How can you quickly fill out a data table for a cubic function?
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By centering the table around the center point and moving two points to the right and left, calculating the y-values based on the power of 3 changes.
What is the parent function for cubic functions?
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The parent function is y = x^3.
How does a negative sign in front of the X^3 affect the graph?
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It reflects the graph over the x-axis.
What happens to the graph if an absolute value symbol is placed in front of the X^3 term?
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The left side of the graph flips over the x-axis, and the negative values become positive, resulting in a graph similar to y = x^2.
How can you draw a rough sketch of y = x^3 + 2?
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Shift the original function y = x^3 up by two units.
How can you draw a rough sketch of y = x^3 - 3?
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Shift the original function y = x^3 down by three units.
How does y = (x - 2)^3 affect the graph's position?
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It shifts the graph two units to the right.
How does y = (x + 4)^3 affect the graph's position?
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It shifts the graph four units to the left.
How does y = (x - 3)^3 affect the graph's position and shape?
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It shifts the graph three units to the right and flips it over the x-axis because of the negative sign.
What is the standard form of a cubic function?
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The standard form is y = a(x - h)^3 + k.
What does 'a' represent in the standard form of a cubic function?
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It determines whether the function is increasing (if a is positive) or decreasing (if a is negative).
What do 'h' and 'k' represent in the standard form of a cubic function?
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H represents the horizontal shift, and K represents the vertical shift of the graph.
How can you accurately graph a cubic function using a data table?
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Center the data table around the center point (h, k), and calculate the y-values by moving points to the right and left of the center.
What is the significance of the center point (h, k) in graphing cubic functions?
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It represents the coordinates where the graph shifts, affecting both the horizontal and vertical positions.
How can you quickly fill out a data table for a cubic function?
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By centering the table around the center point and moving two points to the right and left, calculating the y-values based on the power of 3 changes.
What is the parent function for cubic functions?
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The parent function is y = x^3.