# rca04_CES_0101

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### Introduction to Functions and Graphs :

1.1 Numbers, Data, and Problem Solving 1.2 Visualization of Data 1.3 Functions and Their Representations 1.4 Types of Functions 1.5 Functions and Their Rates of Change Introduction to Functions and Graphs 1

### Numbers, Data and Problem Solving :

Numbers, Data and Problem Solving Classifying numbers Evaluating arithmetic expressions Analyzing the energy produced by your body Evaluating expressions by hand Computing in scientific notation with a calculator 1.1

### Numbers, Data and Problem Solving :

Numbers, Data and Problem Solving Computing with a calculator Finding the speed of Earth Finding the volume of a soda can Calculating the thickness of aluminum foil 1.1

### Teaching Example 1: Classify Numbers :

Slide 1.1 - 5 Copyright © 2010 Pearson Education, Inc. Teaching Example 1: Classify Numbers Classify each real number as one or more of the following: natural number, integer, rational number, or irrational number. −6: integer, rational number Solution

### Teaching Example 1: Classify Numbers :

Slide 1.1 - 6 Copyright © 2010 Pearson Education, Inc. Teaching Example 1: Classify Numbers 9.1: rational number Solution (continued)

### Slide 7:

Slide 1.1 - 7 Copyright © 2010 Pearson Education, Inc. Teaching Example 2: Evaluating Arithmetic Expressions Solution Evaluate.

### Slide 8:

Slide 1.1 - 8 Copyright © 2010 Pearson Education, Inc. Teaching Example 3: Analyzing the Energy Produced by Your Body Solution Write each number in scientific notation. (a) 800 nanovolts, where the prefix nano means one billionth (b) 11.39 watts, the power generated by a person while walking (a) 800 nanovolts = 8  10−7 volts (b) 11.39 = 1.139  101 watts

### Slide 9:

Slide 1.1 - 9 Copyright © 2010 Pearson Education, Inc. Teaching Example 4: Evaluating Expressions by Hand Evaluate each expression. Write your result in scientific notation and standard form. Solution

### Slide 10:

Slide 1.1 - 10 Copyright © 2010 Pearson Education, Inc. Teaching Example 4: Evaluating Expressions by Hand Solution (continued)

### Slide 11:

Slide 1.1 - 11 Copyright © 2010 Pearson Education, Inc. Teaching Example 5: Computing in Scientific Notation with a Calculator Approximate each expression. Write your answer in scientific notation. Solution a.

### Slide 12:

Slide 1.1 - 12 Copyright © 2010 Pearson Education, Inc. Teaching Example 5: Computing in Scientific Notation with a Calculator Solution (continued) b.

### Slide 13:

Slide 1.1 - 13 Copyright © 2010 Pearson Education, Inc. Teaching Example 6: Computing with a Calculator Approximate with a calculator. Solution a. b.

### Slide 14:

Slide 1.1 - 14 Copyright © 2010 Pearson Education, Inc. Teaching Example 7: Finding the Speed of Saturn The radius of the orbit of Saturn is about 887 million miles, and it takes Saturn about 10,767 days to complete one orbit. Estimate the orbital speed of Saturn in miles per hour. Solution Speed S = distance D divided by time T. We need to find the number of miles Saturn travels in 1 year and then divide it by the number of hours in 10,767 days.

### Slide 15:

Slide 1.1 - 15 Copyright © 2010 Pearson Education, Inc. Teaching Example 7: Finding the Speed of Saturn Solution (continued) The distance Saturn travels in one year is The number of hours in 10,767 days is Saturn’s orbital speed is approximately

### Slide 16:

Slide 1.1 - 16 Copyright © 2010 Pearson Education, Inc. Teaching Example 8: Finding the Volume of a Soda Can The volume V of a cylindrical soda can is given by where r is its radius and h is its height. a. If r = 1.5 inches and h = 4.5 inches, find the volume of the can in cubic inches. b. Could this can hold 16 fluid ounces? (Hint: 1 cubic inch equals 0.55 fluid ounce.)

### Slide 17:

Slide 1.1 - 17 Copyright © 2010 Pearson Education, Inc. Teaching Example 8: Finding the Volume of a Soda Can Solution b. To find the number of fluid ounces, multiply the number of cubic inches by 0.55: Yes, the can could hold 16 fluid ounces.

### Slide 18:

Slide 1.1 - 18 Copyright © 2010 Pearson Education, Inc. Teaching Example 9: Calculating the thickness of aluminum foil A rectangular sheet of aluminum foil is 20 cm by 30 cm and weighs 2.7 grams. If 1 cubic centimeter of aluminum foil weighs 2.7 grams, find the thickness of the aluminum foil. Solution Start by making a sketch. Since A = L x W and V = A x T we need to find V and A. Then we will calculate T, using

### Slide 19:

Slide 1.1 - 19 Copyright © 2010 Pearson Education, Inc. Because the foil weighs 2.7 grams and each 2.7 grams equals 1 cubic centimeter, the volume of the foil is 1 cm3. Teaching Example 9: Calculating the thickness of aluminum foil Solution (continued) 