Pre-CalculusChapter 1

Section 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

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

, where A(s) is the area of an equilateral triangle with sides length s.

Find the range of the function

Continuity Continuous Removable discontinuity Jump discontinuity Infinite discontinuity

Increasing and Decreasing Functions

For each function, tell the intervals on which it is increasing and decreasing.

𝑓 (𝑥 )=(𝑥+2)2 𝑔 (𝑥 )= 𝑥2

𝑥2−1

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

x y

-3 9

-2 4

-1 1

1 1

2 4

3 9

For all x in the domain of f,

These are even function.

Symmetric about the x-axis

x y

9 -3

4 -2

1 -1

1 1

4 2

9 3

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

x y

-3 -27

-2 -8

-1 -1

1 1

2 8

3 27

For all x in the domain of f,

This is called an odd function.

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.

Asymptotes

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 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: Complete #79 from page 104

Homework 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