h part below, give a distinct example of a relation that satisfies the criteria,

Question

h part below, give a distinct example of a relation that satisfies the criteria, and give reasons o not use numerical or algebraic answers and don't use examples that we 1 For eac why your example works. D relation. have already used in class. For each, note the domain and the range of the (a) A relation that is a function, whose inverse relation is a function. (b) A relation that is not a function, but whose inverse is a function (c) A relation that is a function, but whose inverse is not a function (d) A relation that is not a function, whose inverse is not a function 2Shoreline's MATH007 class takes place in the ALEKS system, an adaptive, online learning platform. ob in The class gives students a chance to review and test out of pre-college math classes. Part of my j this class is to help students set and meet reasonable goals. At the beginning of the class, each student takes an Initial Knowledge to find out which topics need to be covered At the end of week 1, student A had mastered 150 topics. At the end of week 4, he has mastered 195 topics On the other hand, Student B had mastered 100 topics at the end of week 1 and 160 topics at the end of week 3 Assume that each student continues at the same rate throughout the 11 week term (a) Write functions that describe how m any topics each student will master as a function of number of weeks passed. That is, let t represent the number of weeks into the term and find formulas a(t) and y b(t)on the a() and b() for student A and (b) What are the y-intercepts for each function? What do the y-intercepts represent? (c) When have the two students mastered the same amount of (d) To test into MATH098, the student must master 253 topics. TO test into MATH099, the student B respectively. Sketch a graph of y same axis. topics? must master 389 topics. When, if ever, will each student reach these goals?

Explanation / Answer

1a) a relation that is a function

example is

f(x) = 2x + 3

is a function

and its inverse

f^-1 (x) = (x-3)/2 is also a function

domain is all real values of x (-infinity ,+infinity )

range is all real values of x (-infinity , +infinity )

b) a realation that is not a function but its inverse is a function

f(x) = sqrt (x) is not a function but its inverse domain is [ 0,infinity )

range is [ 0 , infinity )

f^-1 (x) = x^2 is a function

domain is (-infinity , +infinity )

range is [ 0 , infinity )

c) relation that is a function but its inverse if not a function

f(x) = x^2 is a function

but its inverse

f^-1 (x) = + - sqrt x

is not a function

domain is (-infinity , + infinity )

range is [ 0 , infinity )

d) relation that is not a function is

x^2+y^2 = 1 is not a function

and its inverse is also not a function

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