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Do Now

Write the following in interval notation.

1. The numbers between and including 4

and 9.

2. The numbers after 0 (not including 0) upto and including 100.

3. All positive numbers.

4. All negative numbers.

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Objectives C4 & C5AP Calculus AB

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Agenda

1. Review Do Now (5 min)

2. OBJ C4

3. Summary

4. OBJ C5

5. Summary

6. Questions

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C4: Use advanced mathematical notation to

describe properties of functions.

How we communicate the

following on the AP Test?

Domain and Range

Roots / Zeroes

Increasing or Decreasing

Concavity

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C4: Use advanced mathematical notation to

describe properties of functions.

Domain: the x values allowed by

your function.

Range: the y values allowed by

your function.

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C4: Use advanced mathematical notation to

describe properties of functions.

To find domain, it is important to

ask: What x values am I

allowed to plug into the

equation?

Most of the time, it is easier to

ask: What x can I not plug in?

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C4: Use advanced mathematical notation to

describe properties of functions.

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C4: Use advanced mathematical notation to

describe properties of functions.

To find the range, ask a similar

question: What y values can

this function give me?

Or, easier: What y values will I

never get from this function?

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C4: Use advanced mathematical notation to

describe properties of functions.

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C4: Use advanced mathematical notation to

describe properties of functions.

Roots / Zeroes

This is an incredibly important

concept in calculus. It will form

the basis for starting many

problems. They call them roots

for a reason: root of theproblem.

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C4: Use advanced mathematical notation to

describe properties of functions.

A root (aka zero) is where a

function is equal to 0. It is

located at the x values that

cause the function to be zero.

Graphically, this is where the

function crosses the x-axis.

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C4: Use advanced mathematical notation to

describe properties of functions.

Increasing and decreasing.

Many graphs in AP Calculus are

not labeled with numbers. Thismeans we need to get good a

analyzing and describing a

graph verbally.

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C4: Use advanced mathematical notation to

describe properties of functions.

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C4: Use advanced mathematical notation to

describe properties of functions.

Example:

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C4: Use advanced mathematical notation to

describe properties of functions.

Concavity:

A function is concave up when it

is a bowl open upward.

A function is concave down

when it is a bowl opendownwards.

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C4: Use advanced mathematical notation to

describe properties of functions.

Example:

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C4: Use advanced mathematical notation to

describe properties of functions.

Summary:

Precision in calculus depends

on appropriate description.

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C5: Represent a function verbally,

numerically, graphically, or algebraically.

In AP Calc, there are a number ofdifferent ways we will be interpreting

functions. Often, AP graders are less

concerned with the numbers and

more concerned with the concepts.

In addition, this is essential to critical

thinking. If you cannot think about aconcept in a new way, you dont

really understand it.

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C5: Represent a function verbally,

numerically, graphically, or algebraically.

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