Geometry ppl i need help please It’s 13 - 17
It’s unit 2
lesson 2.6 Properties & algebraic proofs

13. You are correct. You multiply the outer 5 with each term inside, and add.

14. The number 0 goes in the first blank and 8 goes in the second blank. So we have 8+0 = 8. The identity property of addition says that adding 0 to any number leads to the same result. In terms of algebra, x+0 = x.

15. The fraction 1/8 goes in the first blank and 1 goes in the second blank. We have the equation 8(1/8) = 1. Multiplying any nonnegative number x with its reciprocal 1/x leads to 1.

16. The number 1 goes in the first blank and -4 goes in the next blank. This property is similar to the property mentioned in problem 14. This time we're working with the multiplicative version. We have the equation -4*(1) = -4

17. The letter a goes in the first blank and x+3 goes in the second blank. So the last equation is a = x+3. The transitive property is the idea of us chaining equations together. It's like saying "if A goes to B, and B goes to C, then A goes to C". Think of it like taking a shortcut bypassing B entirely.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: