Download 5.2 – Evaluate and Graph Polynomial Functions

5.2 – Evaluate and Graph Polynomial
Functions
Recall that a monomial is a number, variable,
or a product of numbers and variables. A
polynomial is a monomial or a sum of
monomials.
A polynomial function is a function of the
form:
5.2 – Evaluate and Graph Polynomial
Functions
an cannot be zero
The exponents are all whole numbers
Coefficients are all real numbers
an is the leading coefficient
n is the degree
a0 is the constant term
A polynomial is in standard form if its terms
are written in descending order of exponents.
5.2 – Evaluate and Graph Polynomial
Functions
5.2 – Evaluate and Graph Polynomial
Functions
Example 1:
Decide whether the function is a polynomial
function. If so, write it in standard form and
state its degree, type, and leading coefficient.
5.2 – Evaluate and Graph Polynomial
Functions
Example 2:
Use direct substitution to evaluate
f(x) = 2x4 – 5x3 – 4x + 8
when x = 3.
5.2 – Evaluate and Graph Polynomial
Functions
Example 3:
Use direct substitution to evaluate
f(x) = x4 + 2x3 +3x2 – 7
when x = -2.
5.2 – Evaluate and Graph Polynomial
Functions
The end behavior of a function’s graph is the
behavior of the graph as x approaches positive
infinity or negative infinity.
For the graph of a polynomial function, the end
behavior is determined by the function’s
degree and the sign of its leading coefficient.
5.2 – Evaluate and Graph Polynomial
Functions
5.2 – Evaluate and Graph Polynomial
Functions
5.2 – Evaluate and Graph Polynomial
Functions