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A Prelude to Functions F. Table of Contents F. Functions and Their Graphs 1. Username Password Forgot your username or password? Pranjul Rastogi.

Let x be the weight in kilograms and let y be the velocity in meters per second. MG 17 Use a graphing utility to find the function of best fit.

Are the results reasonable? Cannons The velocity of a projectile depends upon velocity , and s0 is the initial height of the nose of the many factors, in particular, the weight of the ammunition.

Graph the func- velocity in meters per second. Which gun would be the best for anti-aircraft if Initial the gun were sitting on the ground?

If the guns were on the turret of a ship, MG 17 MG Use exact values. Use your calculator to approximate each value rounded to three decimal places. What shape does the set of points give? What function does this resemble? Fit a sine curve of best fit to the points.

How does that relate to your guess? This is the set of second differences of f1x2. What func- tion does this resemble? Cumulative Review 1. Find an equation for the line containing the points , 52 and 14, What is the distance between these points? What is their midpoint? List the intercepts. Use transformations to graph the equation. This is the set of third differences of f1x2. How does that relate to your 5p guess?

This is the set of fourth differences of f1x2. Plot the points values in part b. Plot the points found? What happened in part f? What func- puted the differences? Explain your answers. Find the real solutions, if any, of the equation 7. Sketch a graph of each of the following functions. Name the inverse func- 2.

Find an equation for the line containing the points , 52 tion of each one and show its graph. Use transformations to graph the equation a cos u b tan u c sin12u2 b - 1.

Do you think the data are linearly c Find the quadratic function of best fit for the third related? Evaluate the equation for e Compute the maximum height for the second bounce. Compute first difference f Compute the maximum height for the third bounce. Why is this result reasonable?

Now j Compare the results from parts h and i. What do you notice about the second differences? Deter- 3z - 1 mine where f is increasing and where f is decreasing. Determine whether the following graph is the graph of 6. Solve the inequality x2 - 3x 6 4 and graph the solution set. Find a linear function with slope -3 that contains the point , Graph the function.

Express your answer in slope-intercept form and graph the line. Determine whether the following relation represents a function: Flag for inappropriate content. Related titles. Jump to Page. We're sorry! We don't recognize your username or password.

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Description For courses in precalculus. This package includes MyLab Math. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Learn more about MyLab Math. Series This product is part of the following series. Preface Preface is available for download in PDF format.

Page references are included for easy review. Now Work "Are You Prepared? These problems appear at the start of each exercise set. Now Work problems —many examples refer to a related problem in the exercise set, which are marked by a yellow pencil icon. If students get stuck while doing their homework, they can look for the closest Now Work problem and refer back to the related example.

These exercises are assignable in MyLab Math. This feature is referenced from the Preparing for This Section feature. Answers appear at the end of the section.

These problems may also require students to utilize skills learned in previous sections, helping them to see how concepts are tied together. They support class discussion, verbalization of mathematical ideas, and writing and research projects. By directing students into essential material, students can focus and retain the most important concepts.

These notes help increase the success of your students in any course structure. They combine problems from previous chapters, providing an ongoing cumulative review. Reach every student with MyLab Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need — when and where they need it — to be successful.

The figures are included in MyLab Math as both a teaching and an assignable learning tool.

From a quick quiz, a personalized, just-in-time review assignment is generated for each student, allowing them to refresh forgotten concepts. This way, students can focus on just the topics they have not yet mastered. Teach your course your way: Your course is unique. Each assignment, handpicked by the author to align with this text, includes a thoughtful mix of question types e. Improve student results: When you teach with MyLab, student performance improves.

New to This Edition. Using the graphing technology students are most familiar with, these images help students visualize concepts clearly and make stronger connections among equations, data and graphs in full color. Table of Contents F. A Prelude to Functions F. Functions and Their Graphs 1. Transformations 1. Constructing Functions 1.

Linear and Quadratic Functions 2. Polynomial and Rational Functions 3.

Exponential and Logarithmic Functions 4. Trigonometric Functions 5. Analytic Trigonometry 6.

Applications of Trigonometric Functions 7. Polar Coordinates; Vectors 8. Analytic Geometry 9. Systems of Equations and Inequalities Substitution and Elimination Matrices Determinants Sequences; Induction; the Binomial Theorem Counting and Probability The Limit, Derivative, and Integral of a Function Review A. Graphing Utilities B.