By Deborah Hughes-Hallett, William G. McCallum, Eric Connally
Shape is expounded to operate. An plane 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 assisting their significant buildings. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial version introduces each one function--linear, energy, quadratic, exponential, polynomial--and provides a learn of the fundamental kind of expressions for that functionality. Readers are inspired to envision the elemental varieties, see how they're developed, and examine the function of every part. in the course of the textual content, there are instruments sections put on the ends of chapters to assist readers gather the abilities they should practice easy algebraic manipulations.
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Additional info for Algebra: Form and Function
5. z Example 6 Solve the equation Solution To undo the operation of dividing by z, we might think about multiplying both sides by z. Since z might be zero, this would not normally be allowed. However, in this case, z cannot be equal to zero in the original equation, since the left-hand side would be undefined. 5. 4. 5. Equivalent Equations Versus Equivalent Expressions Let us compare what we have learned about expressions and equations. To transform an equation into an equivalent equation, we can use any operation that does not change the equality of the two sides.
A2 + b2 and a + b 11. (3 − 4t)/2 and 3 − 2t 2 2 2 8. (a − b)2 and a2 − b2 10. −a + 2 and −(a + 2) 12. bc − cd and c(b − d) 17 17. “Multiply by eighty percent” “Divide by eight-tenths” 18. The area of a triangle is often expressed as A = (1/2)bh. Is the expression bh/2 equivalent to the expression (1/2)bh? 19. Show that the following expressions have the same value at x = −8: 4 13. x + 4x , 5x , and 4x √ 14. (x + 2)2 , x2 + 4, and x4 + 16 In Exercises 15–17, (a) Write an algebraic expression representing each of the given operations on a number b.
If m is the number of males and f is the number of females in a population, which of the following expresses the fact that 47% of the population is male and 53% of the population is female? (a) (c) (e) (g) p1 − p1 + p2 + p3 + p4 + p5 . 5 71. 53f REVIEW EXERCISES AND PROBLEMS FOR CHAPTER 1 In Problems 73–75 assume v tickets are sold for $p each and w tickets are sold for $q each. 73. What does the expression vp + wq represent in terms of ticket sales? 94. Group expressions (a)–(f) together so that expressions in each group are equivalent.
Algebra: Form and Function by Deborah Hughes-Hallett, William G. McCallum, Eric Connally