Which of the following statements best describes the concept of a function ?
For a given input value, there is, at most, one output value.
For given output value, there is, at most, one input value
For given input value, there may be more than one output value.
There is no relationship between the input and output values.
Which of the following best describes the function of the second sentence (“A Dream . . . essayists”) in the context of the passage as a whole?I enjoyed A Dream of Light & Shadow: Portraits of Latin American Women Writers for the same reasons that, as a child, I avidly consumed women’s biographies: the fascination with how the biographical details of another female’s life are represented and line interpreted. 5 A Dream offers a rich read, varied in both the lives and texts of the women portrayed, and the perspectives and styles of the sixteen essayists. Yet, as an adult, I have come to demand of any really “great” book a self-consciousness about the tenuous nature of representations of reality, a critical contextualization of florid detail, and a self-awareness of the role of ideology in our lives. In these critical senses, A Dream is 10 inadequate.To give examples of how A Dream presents fascinating portraits that display awareness of the tenuous nature of representations of reality, To elaborate on how A Dream fulfills the author’s childhood criteria for a pleasurable book, To suggest that the author enjoyed A Dream for reasons more sophisticated than the reasons she enjoyed certain books as a child, To illustrate ways in which the author finds A Dream to be inadequate in certain critical senses, To imply that A Dream is too varied in focus to provide a proper contextualization of the biographical details it offers
You must analyze and graph or sketch this function to answer. This function has 3 roots, at x= 1, -3, and +3. This can be found by factoring first by (x-1) using synthetic division, resulting in a remainder of x^2-9, so it factors to:
(x-1)(x+3)(x-3)
This means there are multiple values of x for a given y, for a portion of the curve, so it is definitely not a one to one function. It actually passes the vertical line test, but not the horizontal line test, so the best answer is that it is a many to one function.
- Ben
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Michael M. answered • 05/14/15
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Hello Kim,
Answers A and D are redundant in that if the equation had failed the vertical line test then it would not have been a function either. So the only remaining answers are one to one function or many to one function. A many to one function has one or more peak(s) and/or valley(s).
The function provided is a polynomial and has a peak and a valley. There are a few ways to show this: Plug in x=-10, -5, 0, 5, 10, etc and compare ups and downs in the evaluations; Take the derivative and see that it is sometimes negative and sometimes positive; or Show that it has multiple roots as Ben did. If a function has multiple roots then there must be a peak or valley between each. Likewise, if the derivative shifts from negative to positive or vice versa then there's an up-slope and down-slope with a peak of valley between them.
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Occupation specific capability sets describe specialised capabilities for professional, technical or trade-related roles. These can be used to complement the Capability Framework where roles require specialised capabilities.
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