Question

Given the equation y=(the square root of) x+9, what domain will produve a range that is in the set of real numbers

Answer 1

Think about it another way: what domain will give us non-real (imaginary) numbers? As it's a square root, we're looking to square root a negative number so x<-9. As we're looking for real numbers, take the opposite of this and we get x>=-9 :) You can double check your domain:
x=-9 => f(-9)=0 Real
x=-8 => f(-8)=+-1 Real
x=-7 => f(-7)=sqrt(2) Real
And so on, we can clearly see the numbers are getting bigger and remaining real.

Answer 2

Neither, the function gives real numbers when x is greater than or equal to -9. x>=-9

Answer 3

What is the range? Your function is f(x)=(x-5)/(x+8), yes?

Answer 4

yeah, the range is the set of real numbers

Answer 5

and then also my last question is given the relation y=x^2-4 state the range if the domain is {-2, -1, 0, 1, 2}

Answer 6

Your domain is just x≠-8 as you don't want to divide by 0. Any other number gives a real number as an output - try some values of x in the expression and you'll see.

As for the other one. Put each number in:

f(x)=x^2-4
f(-2)=0
f(-1)=-3
f(0)=-4
f(1)=-3
f(2)=0

So our range is {-4, -3, 0}

Answer 7

thanks so much!! and sorry this is the last question but theres one that says state the range if the domain is {x-2 < or equal to x < or equal to 2}

Answer 8

so the domain is \[\Large -2 \le x \le 2\] right?

Answer 9

it says x-2 for the first one

Answer 10

theres just an x before the -2

Answer 11

ok so

\[\Large x-2 \le x \le 2\]

right?

Answer 12

yeah

Answer 13

ok you have to break up the compound inequality into these two inequalities

\[\Large x-2 \le x\]

and

\[\Large x \le 2\]

Answer 14

what do you get when you solve \[\Large x-2 \le x\] for x

Answer 15

not sure...would it be -2?

Answer 16

well if you subtract x from both sides, you get

\[\Large -2 \le 0\]

which is always true

Answer 17

right

Answer 18

so it turns out the solution to \[\Large x-2 \le x \le 2\] is \[\Large x \le 2\]

Answer 19

your domain is \[\Large x \le 2\]

Answer 20

thanks so much! got it!

Answer 21

use that to find the range

Answer 22

how would you do that?

Answer 23

is it < or equal to 3?

Answer 24

what is the original function again? can you draw it out?

Answer 25

\[y=x ^{2}\]

Answer 26

I thought it was a square root or something?

Answer 27

oh no sorry that was a different one! i thought you were helping with the second question

Answer 28

the question is state the range if the domain is \[x-2\le x \le 2\]

Answer 29

ok so as shown above, the domain simplifies to \[\Large x \le 2\]

Answer 30

so graph y = x^2 using a graphing calculator like this one

https://www.desmos.com/calculator

Answer 31

however, only graph when x <= 2

so you will type in "x^2{x<=2}" without quotes

the {x<=2} ensures only the portion to the left of x=2 is graphed (x=2 is included)

Answer 32

you then use the graph to determine the range