Question

graph the function f(x)=sqrt(x+3) +4 on a grid. Label at least 3 points and state the domain and range in interval notation. Step by Step please?

Answer 1

Pick some points and calculate the value of f(x)
I suggest x = -3, -2, 1

Answer 2

This is where i end up getting stuck at. I understand when I substitute the -3 in for x I get a point of (-3, 4) but then when I substitute -2 in I get the square root of -1 +4 which confuses me. Do I ignore the square root and simply use -1+4 to come up with the points (-2,3)? Thank you SO much for your help.

Answer 3

f(x) = sqrt(x+3) + 4
if x = -3; f(x) = sqrt(-3 + 3) + 4 = 4

Answer 4

oops, I see now. I ignore the square root and with x=-2 the points are (-2, 5) is that correct? Now do you know how to find the domain and range from this

Answer 5

if x = -2; f(x) = sqrt(-2 + 3) + 4 = 1 + 4 = 5

Answer 6

Alright, now I understand finding the points. From here, how to find the domain and range?

Answer 7

For a square root problem, if the term inside the square root is < 0, there is no solution. That means x can't be < -3.

Answer 8

But x could be as large as +infinity

Answer 9

I'm not sure how they want you to present that, something like [3, infinity] ?

Answer 10

so now that I understand the domain, how do I get the range? she has (4, infinity) but I don't understand how she got that

Answer 11

What is the smallest possible value for y?

Answer 12

the smallest possible value for y is 4

Answer 13

So that's where the 4 in the range comes from.

Answer 14

can you plug any number into this to check the answer? My partner is telling me that she is confused because if she plugs 2 into the original equation she gets 9 for (2,9) and that "isn't on the line". does it matter that it isn't on the line?

Answer 15

Two problems:
f(2) is not 9
it's not a line

Answer 16

how am I suppose to know what to plug in?

Answer 17

Umm I was just responding to your partner's issues. We're almost done. Can you see that f(2) is not equal to 9?

Answer 18

I think so. All I keep seeing is that when I use f(2) it equals sqrt 2+3 +5, so wouldn't that equal 9 or am I missing this all together?

Answer 19

oops I mean 2+3 +4 not 2+3+5

Answer 20

f(x)=sqrt(x+3) +4
That's what you entered.
So the parentheses mean that if x = 2, we add 2 + 3 and get 5 and then do sqrt(5)
The +4 is later.

Answer 21

so when I use f(2) i should get a y of the square root of 5? 2.24?

Answer 22

plus the 4

Answer 23

+4 so it would be (2,6.24)?

Answer 24

Yes

Answer 25

THANK YOU!!!!

Answer 26

yw