Namer Class Time: Math 1110: Reading Assignment for Section 1.2 Attach this cove

Question

Namer Class Time: Math 1110: Reading Assignment for Section 1.2 Attach this cover sheet to your work. Be sure to answer all the questions completely on a separate page. I highly recommend reading all of the questions before answering any of them since often questions relate to each other Equivalent expressions are expressions in which any arbitrary input value produces the same output value for all of the expressions. In the appendix G activity we showed several pairs of expression were not equivalent by finding an input value that produces different output values, which could have been found using a graphing calculator in graphing mode or table mode. 1. Using the table feature of a graphing calculator, how can one show that two expressions/functions 2. 3. are not equivalent? How can one graphically show that two expressions/functions are not equivalent? Warning: Checking values cannot show two expressions are equivalent. Explain why someone cannot use the table feature of a graphing calculator to prove two expressions are equivalent. Use the following two expressions to clarify your explanation: 2x (3x+5) and 2 a. 3x+5 Hint : Evaluate both expressions at x- Explain why the warning means that someone cannot use the graphing feature of a graphing calculator to prove two expressions are equivalent. Use the following two expressions to clarify your explanation:+1 and x + 11. Note that the first expression is the absolute value of the quantity x+ 11 and that the absolute value function is located under the math menu of your calculator: abs( Hint: Look at the standard view window and then a view window to b. the left ofx- -10. 4. Use the distributive property of muliplication over adition to show that 1+x is equivalent to + Be sure to state or explicitly show where you used the distributive property. Example 4 in . , , Appendix A.2 will be helpful. 5. Is 12 equivalent taquivalen, what val orationo) transfoms one into x+1 the other? If they are not equivalent, provide an input value that produces different output values for the two expressions There are graphing caleulator directions on the math 1110 webpage. Also, youtube has a wealth of information about using a graphing calculator; simply search your calculator model and graphing functions. For more information about expressions, visit Khan Academy https:/www.khanacademy.org/math/algebra/introduction-to-algebra There is also an app for Khan Academy for tablets and smart phones. You can view the videos (not the quizzes) by going to Math, Algebra I, and then Introduction to algebra. 37

Explanation / Answer

(1) Use graphing calculator for this question.

(2) Two expressions/ functions are not equivalent if their graphs are not identical.

(3) Checking of values can show that the two expressions / functions are identical provided it is performed for all inputs in the definition of the domain of the function. This can be done for all finite elements domain functions. For infinite elements domain functions checking is not feasible (in general).

(a) Since, the domain i.e. which values x can assume is not provided in the problem (it may be set of integers, real, a finite set or any other set), and as table feature can be used for only finite number of elements (not too large). Hence, we can not use the table property to prove equivalence of functions as one given in example.

Note that the two given expressions are equivalent if 3x + 5 not equal to zero i.e. x is not equal -5/3, otherwise the functions are not equivalent.

(b) Note that for using graphing feature the functions must be well defined in the domain otherwise this feature can not be used.

4. (1 + x) / 2 = 1/2 + x/2 [By distributive property of division over addition.

5. Addition does not distributive over division or multiplication (these operations are above in hierarchy of operations than Addition or Subtraction. The parentheses overrule this heirarchy of operations. Therefore, fiirst x and 1 will be added and then only 2 will be divided by (x+1).

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