Families of Polynomials Graph the family of polynomials in...

Families of Polynomials Graph the family of polynomials in the same viewing rectangle, using the given values of c.
Explain how changing the value of c affects the graph.
$$
P(x)=(x-c)^{4} ; \quad c=-1,0,1,2
$$

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Key Concepts

Horizontal Translation

Horizontal translation is a specific type of function transformation where the entire graph of a function is shifted left or right along the x-axis. For the polynomial P(x) = (x - c)^4, altering the value of c shifts the graph right when c is positive and left when c is negative, without changing its shape or the rate at which it ascends or descends.

Families of Polynomial Functions

This concept pertains to a group of polynomial functions that are defined by an algebraic expression with one or more parameters. These parameters, such as c in the polynomial P(x) = (x - c)^4, allow the entire family of graphs to be studied collectively as they respond similarly to changes in the parameter.

Function Transformations

Function transformations involve changes to a function's formula that result in predictable shifts, stretches, compressions, or reflections of its graph. In the context of the polynomial given, the parameter c affects the graph by translating it horizontally.

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