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Pre-Calculus Chapter 1 Section 1 & 2. Modeling with Equations and Solving Functions and Their Properties 2013 - 2014.

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pre calculus chapter 1 section 1 2

Pre-CalculusChapter 1Section 1 & 2

Modeling with Equations and Solving

Functions and Their Properties

2013 - 2014


A pizzeria sells a rectangular 20” by 22” pizza for the same amount as a large round pizza (24” diameter). If both pizzas are the same thickness, which option gives you the most pizza for the money

The engineers at an auto manufacturer pay students $0.08 per mile plus $25 per day to road test their new vehicles.

How much did the auto manufacturer pay Sally to drive 440 miles in one day?

John earned $93 test-driving a new car in one day. How far did he drive?

things you should know about functions
Things you should know about Functions
  • Domain:
  • Range:
  • Function:
  • Vertical Line Test:

Input values, x, independent

Output values, y, dependent

Each domain value has 1 y value

A graph is a function if a vertical line passes through it and only intercepts at 1 point

find the domain of the functions
Find the domain of the functions
  • , where A(s) is the area of an equilateral triangle with sides length s.
  • Continuous
  • Removable discontinuity
  • Jump discontinuity
  • Infinite discontinuity
local and absolute extrema
Local and Absolute Extrema
  • Local values are located on an interval. Absolute values are the highest or lowest on the whole graph
    • Local maximum is the highest point in a section of a graph. If it is actually the highest point, it is the absolute maximum.
Decide whether has any local maxima or local minima. If so, find each maximum or minimum value and the value of x at which it occurs.
symmetric about the y axis
Symmetric about the y-axis

For all x in the domain of f,

These are even function.

symmetric about the x axis
Symmetric about the x-axis

These are not true functions because they fail the vertical line test.

You can say (x, -y) is on the graph when (x, y) is on the graph.

symmetric about the origin
Symmetric about the origin

For all x in the domain of f,

This is called an odd function.

checking symmetry
Checking symmetry
  • To check if a function is an even function, subsitute (-x) in for x. If the function is the same, it is even.
  • To check if a function is odd, substitute (-x) in for x. If the function is the opposite sign of the original function, it is odd.
  • If the rules applied does not fit an even nor odd function, you would say the function is neither.
  • An asymptote is an imaginary line where the function does not exist. It can forever get closer to that line but will never actually touch the line.
finding asymptotes
Finding Asymptotes
  • If a function is in fraction form, set the denominator equal to 0 to find vertical asymptotes.
  • Set the whole function equal to zero to find the horizontal asymptotes.
before you leave today
Before you leave today:
  • Complete #79 from page 104
  • Ch 1.1; Pg. 81-83: 1-10, 22, 29, 31
  • Ch 1.2; Pg. 102-103: 1-25 every other odd, 41 – 61 every other odd, 73