What restrictions must be made on x, y, and z so that the triple (x, y, z) will represent a point on the y axis? on the z axis? in the xz plane? in the yz plane?

The point in y-axis are  ,  the point at z -axis are, , the point at xz -plane are, and the point at xz -plane are, .

Given-

i) The point (x, y, z) will represent a point on the y axis -As we know that on the y-axis the other two coordinates will have no point or zero points. Thus at y-axis-

Hence the point at y -axis will be,

II)  The point  (x, y, z) will represent a point on the z axis -As we know that on the z-axis the other two coordinates will have no point or zero points. Thus at z-axis-

Hence the point at z -axis will be,

III)  The point (x, y, z) will represent a point  In the xz plane-

In the xz-plane both x and z keeps some value but the y coordinate will be zero in xz plane. Thus In the xz plane-

Hence the point at xz -plane will be,

iv)The point  (x, y, z) will represent a point  In the yz plane-

In the yz-plane both x and z keeps some value but the y coordinate will be zero in yz plane. Thus In the yz plane-

Hence the point at xz -plane will be,

Hence, the point in y-axis are  ,  the point at z -axis are, , the point at xz -plane are, and the point at xz -plane are, .

For more about the coordinate plane follow the link below-

link

i) The point on y-axis is (0,y,0)

            ii) The point on z-axis is (0,0,z)

            iii)  The point on x z plane is (x,o,z)

            iv) The point on y z plane is (0,y,z)

Step-by-step explanation:

Explanation:-

i) For every point on x-axis, y-co-ordinate is zero and z- co-ordinate is zero

i .e., y=0 and z=0

The point on x-axis is (x,0,0)

ii) For every point on y-axis, x-co-ordinate is zero and z- co-ordinate is zero

i .e., x=0 and z=0

The point on y-axis is (0,y,0)

iii) For every point on z-axis, x-co-ordinate is zero and y- co-ordinate is zero

i .e., x=0 and y=0

The point on z-axis is (0,0,z)

iv)  For every point on X Z plane then Y=0

The point on x z plane is (x,o,z)

v) For every point on Y Z plane then X=0

The point on yz plane is (0,y,z)

vi) For every point on X Y plane then Z=0

The point on x y plane is (x,y,0)

no he doesnt because "-16' is negatiive

step-by-step explanation:

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: