Question

x=(y+2)^2
give the domain and range
and graph

Answer 1

Immediate inspection for part of it. \(x \ge 0\). Do you see why this is obvious?

Answer 2

nope

Answer 3

When squaring Real Numbers, what is the result? Positive? Negative? Zero?

Answer 4

whichever right?

Answer 5

lol

Answer 6

(1)^2 = 1
(-1)^2 = 1
(2)^2 = 4
(-2)^2 = 4
(3)^2 = 9
(-3)^2 = 9

See any negative numbers on the right-hand side?

Answer 7

ohh yeahh no there are no negatives

Answer 8

That's it. So that (y+2)^2 CANNOT be NEGATIVE. Makes sense?

Answer 9

yup lol

Answer 10

This gives the Domain: \(x\ge 0\).

How about the Range? What values for 'y' are acceptable?

Answer 11

any. but i put in -1, 0, 1, and 2

Answer 12

You can "put in" until your paper runs out. Any value will do. This gives the Range \(-\infty<y<\infty\)

Answer 13

okay, so how can i graph it. do i just plug in the numbers for y and graph it?

Answer 14

You should pick a few values around y = -2, maybe y = -4, -3, -2, -1, 0 and get a feel of it. You should not need more than that.

See if you can figure out why I selected y = -2 as the central value.

Answer 15

those are the numbers that chose to plug in after i saw how big the result was for the others. the central value is -2 because it equals 0

Answer 16

It is hoped that you can look at the original equation and see that this is so. y = -2 ==> x = 0. It is a good thing to notice right up front.