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3 years ago

Which of the following sets are closed under subtraction? Select all that apply.

Mathematics

2 answers:

Vanyuwa [196]3 years ago

7 0

only integers and polynomials are under subtraction.

Rina8888 [55]3 years ago

4 0

Answer:

Integers

Polynomials

Step-by-step explanation:

A set is closed under an operation if performance of that operation on members of the set always produces a member of that set.

so, closed under subtraction means if we subtract two numbers of a set than it must belong to that set.

Integers: They are closed under subtraction.

since, if we subtract two integers it will be an integer only.

Irrational numbers: They are not closed under subtraction.

example- 2+√2 and √2 are two irrational numbers but 2+√2-√2=2 which is not an irrational number

Whole numbers: They are not closed under subtraction.

example- 1 and 2 are whole numbers but 1-2= -1 is not an whole number.

Polynomials: They are closed under subtraction.

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3 years ago

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2 years ago

Ava graphs the function h(x) = x2 + 4. Victor graphs the function g(x) = (x + 4)2. Which statements are true regarding the two g

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Using translation concepts, the correct statements are given as follows:

Ava's graph is vertical translation of x².

Ava's graph has a y-intercept of 4.

Victor's graph moves 4 units from f(x) = x² in a positive direction.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

Ava's graph is given by:

h(x) = x² + 4.

It is a vertical translation of 4 units of f(x) = x², as the change was in the range of the function. Hence, it has a y-intercept of f(0) = 0² + 4 = 4.

Victor's graph is given by:

g(x) = (x + 4)²

Which means that it moves 4 units from f(x) = x² in a positive direction.

More can be learned about translation concepts at brainly.com/question/4521517

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