Polynomial and Rational Functions (PR)

Chapter 4 Polynomial and Rational Functions (PR)

Objectives

How do we model polynomial or rational change?

By the end of this chapter, you should be able to...

Graph quadratic functions and identify their axis of symmetry, and maximum or minimum point.
Use quadratic models to solve an application problem and establish conclusions.
Determine the zeros and their multiplicities of a polynomial in factored form. Describe and graph the behavior of a polynomial function at the intercepts and the ends.
Rewrite a rational function as a polynomial plus a proper rational function.
Determine the zeros of a polynomial function with real coefficients.
Find the domain and range, vertical and horizontal asymptotes, and intercepts of a rational function and use this information to sketch the graph.

Readiness Assurance.

Before beginning this chapter, you should be able to...

Evaluate functions from an equation.
- Review and Practice: Khan Academy
  ¹
  www.khanacademy.org/math/college-algebra/xa5dd2923c88e7aa8:functions/xa5dd2923c88e7aa8:evaluating-functions/v/understanding-function-notation-example-1
- Review and Practice: Section 2.2
  ²
  FN2
Find the intercepts of a line.
- Review and Practice: Khan Academy
  ³
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:x-intercepts-and-y-intercepts/v/introduction-to-intercepts
Find the intercepts of a graph of a function.
- Review and Practice: Section 2.3
  ⁴
  FN3
Find the degree and leading coefficient of a polynomial.
- Review and Practice: Khan Academy
  ⁵
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-monomial-polynomial/v/polynomials-intro
Determine if a graph is a polynomial function.
- Review: YouTube (Math Tutorials)
  ⁶
  youtu.be/lv4N59OQxss?si=0NMXefTqImRqQRHr
Determine where a function is increasing and decreasing.
- Review and Practice: Khan Academy
  ⁷
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:intervals-where-a-function-is-positive-negative-increasing-or-decreasing/v/increasing-decreasing-positive-and-negative-intervals
Find the equation of a line given two points.
- Review and Practice: Khan Academy
  ⁸
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb11595b61c86:writing-slope-intercept-equations/v/equation-of-a-line-3
- Review and Practice: Section 3.2
  ⁹
  LF2
Factor quadratics and polynomials.
- Review and Practice (Quadratics): Khan Academy
  ¹⁰
  www.khanacademy.org/math/college-algebra/xa5dd2923c88e7aa8:quadratics-multiplying-and-factoring/xa5dd2923c88e7aa8:factoring-quadratics-intro/v/factoring-simple-quadratic-expression
- Review and Practice (Polynomials): Khan Academy
  ¹¹
  www.khanacademy.org/math/college-algebra/xa5dd2923c88e7aa8:polynomial-arithmetic/xa5dd2923c88e7aa8:factoring-higher-degree-polynomials/v/factor-high-deg-poly
Perform long division of two whole numbers.
- Review and Practice: Khan Academy
  ¹²
  www.khanacademy.org/math/arithmetic-home/multiply-divide/multi-digit-div/v/long-division-without-remainder
Solve quadratic equations with complex roots.
- Review and Practice: Khan Academy
  ¹³
  www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-eq/v/complex-roots-from-the-quadratic-formula
- Review and Practice: Section 1.5
  ¹⁴
  EQ5
Simplify rational expressions.
- Review and Practice: Khan Academy
  ¹⁵
  www.khanacademy.org/math/algebra-home/alg-rational-expr-eq-func/alg-simplify-rational-expressions/v/simplifying-rational-expressions-introduction

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