Key Features of Cubic Functions

Front

What is the Range of ALL Cube Root Functions in interval notation?

Back

(−∞,∞)

Front

Determine the roots of the polynomial: f(x) = (x+1)(x-4)(x+2)

Back

-1, 4, -2

Front

Determine the roots of the polynomial: f(x) = (x-2)(x+3)²

Back

2, -3

Front

What is/are the zero(s) of the function f(x) = (x+4)(x+1)(x-2)?

Back

x = -4, x = -1, x = 2

Front

What is the y-intercept of the following cubic function: f(x) = x³ - 3x + 2?

Back

(0, 2)

Front

What is a cubic function?

Back

A polynomial function of degree three, generally expressed as f(x) = ax³ + bx² + cx + d.

Front

What are the characteristics of the graph of a cubic function?

Back

It can have one or two turning points and can cross the x-axis up to three times.

Front

What is the leading coefficient test for cubic functions?

Back

If the leading coefficient (a) is positive, the graph rises to the right; if negative, it falls to the right.

Front

How do you find the y-intercept of a cubic function?

Back

Substitute x = 0 into the function.

Front

What is the significance of the roots of a polynomial?

Back

Roots are the x-values where the function equals zero, indicating where the graph intersects the x-axis.