Key Features of Functions

Front

What are the factors of a cubic function with zeros -1, 1, and 4?

Back

(x + 1)(x - 1)(x - 4)

Front

How many roots does a cubic function with three distinct zeros have?

Back

3

Front

What are the factors of a polynomial function with zeros at -3, 0, and 4?

Back

x(x + 3)(x - 4)

Front

How do you find the x-intercepts of a function?

Back

Set the function equal to zero and solve for x.

Front

What are the x- and y-intercepts of a function?

Back

x-intercepts are points where the graph crosses the x-axis (y=0), y-intercepts are points where the graph crosses the y-axis (x=0).

Front

What is the relationship between the degree of a polynomial and the number of roots it can have?

Back

A polynomial of degree n can have at most n roots.

Front

What is a zero of a function?

Back

A zero of a function is a value of x that makes the function equal to zero.

Front

How do you determine the factors of a polynomial from its zeros?

Back

For each zero, (x - zero) is a factor of the polynomial.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial graph.

Front

What does it mean for a function to be factored completely?

Back

A function is factored completely when it is expressed as a product of its linear factors.