By Deborah Hughes-Hallett, William G. McCallum, Eric Connally

Shape is said to operate. An aircraft wing has the shape it does as a result of its lifting functionality. The pillars of the Parthenon and the girders of a skyscraper are formed to the aim of helping their substantial buildings. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial variation introduces each one function--linear, energy, quadratic, exponential, polynomial--and offers a research of the elemental type of expressions for that functionality. Readers are inspired to ascertain the fundamental types, see how they're developed, and look at the function of every part. during the textual content, there are instruments sections put on the ends of chapters to assist readers gather the talents they should practice uncomplicated algebraic manipulations.

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**Additional info for Algebra: Form and Function**

**Example text**

30. Professor Priestley calculates your final grade by averaging the number of points, x, that you receive on the midterm with the number of points, y, that you receive on the final. Professor Alvorado takes half the points on each exam and adds them together. Are the two methods the same? Explain your answer algebraically. 31. Your older sister, who has more money than you, proposes that she give you half the difference between the amount of money, $q, that she has and the amount of money, $p, that you have.

This step does not produce an equivalent equation because x might be equal to zero. In fact, both x = 3 and x = 0 are solutions to the first equation, but only x = 3 is a solution of the second equation. When we divide by x, we lose one of the solutions of the original equation. Since it is not helpful to lose solutions to an equation, dividing both sides of an equation by an expression that could take the value zero is not regarded as a valid step in solving equations. 4 EQUIVALENT EQUATIONS 21 Deciding Which Operations to Use In Example 2 we chose an operation that produced an equation of the form x = Number.

4. 60. 9. y − 4 = 3y 12 Chapter 1 THE KEY CONCEPTS OF ALGEBRA In Exercises 10–15, is the value of the variable a solution to the equation? 10. t + 3 = t2 + 9, t = 3 11. x+3 = x2 −9, x = −3 12. x + 3 = x2 − 9, x = 4 13. 14. a+3 a−3 = 1, a = 0 3+a = 1, a = 0 3−a 21. Which of the following are equations? (a) (b) (c) (d) 3(x + 5) = 6 − 2(x − 5) ax2 + bx + c = 0 5(2x − 1) + (5 − x)(x + 3) t = 7(t + 2) − 1 22. (a) Construct a table showing the values of the expression 1 + 5x for x = 0, 1, 2, 3, 4. (b) For what value of x does 1 + 5x = 16?