5 1 Polynomial Functions Learning goals graph functions
- Slides: 13
5. 1 Polynomial Functions Learning goals • graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. • graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
monomial : a number, a variable, or the product of a real number and variables with whole number exponents polynomial : a monomial or the sum of monomials Vocabulary degree : For a monomial – the sum of its exponents For a polynomial – the largest sum of exponents from a term **Always put answers in standard form: descending order of exponents
By # of Terms 1 – monomial 2 – binomial 3 – trinomial 4 or more - polynomial Classifying Polynomials By Degree 0 – constant 1 – linear 2 – quadratic 3 – cubic 4 – quartic 5 – quintic Shape
Ex 1 Put in standard form What is the degree of the polynomial? Classify each polynomial by degree and number of terms What shape is it?
Ex 2 Write in standard form, classify, state degree and shape.
The degree of a polynomial function affects the shape of its graph the maximum number of turning points the way behaves at its ends Vocabulary turning point : places where a graph changes direction end behavior : direction of the graph where the arrows appear (far left and far right of the graph)
Vocabulary relative minimum /relative maximum peaks and valleys within the graph of a polynomial that has several turning points
Ex 3 Find the relative minimum and maximum
End Behavior a a behaves is positive is negative like n is even up and up (n≠ 0) n is odd down and up down and down parabola up and down line
Ex 4 Describe the end behavior Is the graph odd or even? Is the leading coefficient positive or negative? Relative max or min?
Ex 5 Describe the end behavior Is the graph odd or even? Is the leading coefficient positive or negative? Relative max or min?
Ex 6 For each polynomial function: describe the end behavior sketch
Ex 7 For each polynomial function: describe the end behavior sketch
- Strategic goals tactical goals operational goals
- Strategic goals tactical goals operational goals
- Evaluate and graph polynomial functions
- Numpy.polynomial.polynomial
- How to divide a polynomial by another polynomial
- General goals and specific goals
- Motivation in consumer behaviour
- Cuadro comparativo de e-learning
- Quartic polynomial graph
- Degree and leading coefficient
- Transformation polynomial functions
- Review of polynomials and polynomial functions
- Polynomial function graph
- Positive or negative coefficient graph