Functions (FN)

Chapter 2 Functions (FN)

Objectives

BIG IDEA for the chapter goes here, in outcomes/main.ptx

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

Determine if a relation, equation, or graph defines a function using the definition as well as the vertical line test.
Use and interpret function notation to evaluate a function for a given input value and find a corresponding input value given an output value.
Use the graph of a function to find the domain and range in interval notation, the \(x\)- and \(y\)-intercepts, the maxima and minima, and where it is increasing and decreasing using interval notation.
Apply transformations including horizontal and vertical shifts, stretches, and reflections to a function. Express the result of these transformations graphically and algebraically.
Find the sum, difference, product, quotient, and composition of two or more functions and evaluate them.
Find the inverse of a one-to-one function.

Readiness Assurance.

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

Use interval notation for solutions.
- Review:
  - Introduction to Interval Notation
    ¹
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:introduction-to-the-domain-and-range-of-a-function/v/introduction-to-interval-notation
  - Inequalities and Interval Notation
    ²
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:multistep-inequalities/v/multi-step-inequalities
- Practice:
  - Linear Inequalities
    ³
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:multistep-inequalities/e/linear_inequalities
Use substitution.
- Review:Substitution
  ⁴
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:substitute-evaluate-expression/v/evaluating-expressions-in-two-variables
- Practice: Substitution
  ⁵
  www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:intro-variables/e/evaluating_expressions_1
Apply order of operations.
- Review:
  - Introduction to order of operations
    ⁶
    www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-order-of-operations/v/introduction-to-order-of-operations
  - Order of operations
    ⁷
    www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-order-of-operations/v/more-complicated-order-of-operations-example
- Practice:
  - Order of operations
    ⁸
    www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-order-of-operations/e/order_of_operations
  - Order of operations 2
    ⁹
    www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-order-of-operations/e/order_of_operations_2
Create a table from a function.
- Review:
  - Create table
    ¹⁰
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/descartes-and-cartesian-coordinates
- Practice:
  - Graph points
    ¹¹
    www.khanacademy.org/math/cc-sixth-grade-math/x0267d782:coordinate-plane/cc-6th-coordinate-plane/e/identifying_points_1
Combine like terms.
- Review:
  - Combine like terms
    ¹²
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:combine-like-terms/v/combining-like-terms
  - Combine like terms 2
    ¹³
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:combine-like-terms/v/combining-like-terms-and-the-distributive-property
- Practice:
  - Combine like terms
    ¹⁴
    www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-combining-like-terms/e/combining-like-terms-0.5
  - Combine like terms 2
    ¹⁵
    www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:combine-like-terms/e/manipulating-linear-expressions-with-rational-coefficients

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