A13 - Cubic Functions

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•
Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a cubic function?
Back
A cubic function is a polynomial function of degree three, typically expressed in the form: f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.
2.
FLASHCARD QUESTION
Front
What is the general shape of a cubic function's graph?
Back
The graph of a cubic function can have one or two turning points and can extend to positive or negative infinity in both directions. It typically has an 'S' shape.
3.
FLASHCARD QUESTION
Front
What is the y-intercept of a function?
Back
The y-intercept of a function is the point where the graph intersects the y-axis, which occurs when x = 0.
4.
FLASHCARD QUESTION
Front
How do you find the y-intercept of a cubic function?
Back
To find the y-intercept of a cubic function, substitute x = 0 into the function and solve for y.
5.
FLASHCARD QUESTION
Front
What does the leading coefficient of a cubic function determine?
Back
The leading coefficient (the coefficient of the x^3 term) determines the end behavior of the cubic function's graph. If it's positive, the graph rises to the right; if negative, it falls to the right.
6.
FLASHCARD QUESTION
Front
What is a turning point in a cubic function?
Back
A turning point is a point on the graph where the function changes direction from increasing to decreasing or vice versa.
7.
FLASHCARD QUESTION
Front
What is the significance of the roots of a cubic function?
Back
The roots (or zeros) of a cubic function are the x-values where the function equals zero. They represent the x-intercepts of the graph.
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