This chapter covers functions, equations, and graphs. It defines functions and function notation. Students will learn to graph relations and identify functions. They will also learn to write and interpret direct variation equations. The chapter discusses representing relations with ordered pairs, tables, mappings, and graphs. It defines domain and range and teaches how to determine if a relation is a function using the vertical line test. Students will work with function rules and notation to evaluate functions for given inputs. Examples are provided to model real-world scenarios with functions.
2. Essential Understanding: a pairing of items from
tow sets is special if each item from one set pairs
exactly with one item from the second set.
Essential Understanding: some quantities are in
a relationship where the ratio of corresponding
values is constant
Objectives:
Students will be able to graph relations
Students will be able to identify functions
Students will be able to write and interpret direct
variation equations
3. Functions – (Review)
F-IF.1. Understand that a function from one set (called
the domain) to another set (called the range) assigns
to each element of the domain exactly one element of
the range. If f is a function and x is an element of its
domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the
graph of the equation y = f(x).
F-IF.2. Use function notation, evaluate functions for
inputs in their domains, and interpret statements that
use function notation in terms of a context.
4. Algebra
A-CED.2. Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate
axes with labels and scales.
Functions
F-IF.1. Understand that a function from one set (called the domain)
to another set (called the range) assigns to each element of the
domain exactly one element of the range. If f is a function and x is
an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the
equation y = f(x).
F-BF.1. Write a function that describes a relationship between two
quantities.★ Determine an explicit expression, a recursive process,
or steps for calculation from a context.
5. Set of pairs of input and output values
Represented in four different ways
Ordered Pair Mapping Diagram
Table of Values Graph
6. The monthly average water temperature of
the Gulf of Mexico in Key west, Florida varies
during the year. In January, the average
temperature is 69 degrees, in February, 70
degrees, in March, 75 degrees, and in April, 78
degrees. How can you represent this
relation?
7. What is domain?
Input values of a relation/function (x-coordinates)
What is range?
Output values of a relation/function (y-
coordinates)
What is the domain and range of the relation?
{(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)}
8. A relation in which each element of the
domain corresponds with exactly one
element of the range.
9. On a graph you can use the vertical line test
to determine if the relation is a function.
10. Function Rule: an equation that represents
an output value in terms on an input value
Function Notation: uses f(x) = equation
Independent Variable: x, represents the
input of a function
Dependent Variable: f(x) or y, represents the
output of a function
For f(x) = -4(x) + 1, what is the output for the
given inputs: -2, 0, and 5?
11. A pizza costs $14; the flat delivery fee is
$1.50. What function rule models the total
cost of the number of pizzas delivered.
Evaluate for 5 pizzas.
