Question

what are the domain and range of the function

Answer 1

\[2\sqrt{3x+4} -5\]

Answer 2

i understand the domain part

Answer 3

(Assuming real numbers are in work here.)

Square roots output positive numbers or real on their domain.
That is,
\[\sqrt{u} \ge 0 \\ \text{ that is the range of } \sqrt{u} \text{ is } [0,\infty)\]

Answer 4

now pretend we have
\[ 2 \sqrt{u} \ge 0 \\ \text{ this still means } \\ \sqrt{u} \ge 0 \\ \text{ so the range of } 2 \sqrt{u} \text{ is still } [0,\infty)\]

Answer 5

now what happens if you subtract 5 on both sides of that inequality

Answer 6

\[\sqrt{u} \ge 0 (\text{ note: range is } [0,\infty) \\ \\ \text{ multiply both sides of } 2 \\ 2 \sqrt{u} \ge 0 ( \text{ note: range is } [0,\infty) \\ \\ \text{ now see what your inequality says when you subtract 5 on both sides }\]

Answer 7

would it be \[y \ge 5\]

Answer 8

did you subtract 5 on both sides?

Answer 9

ok but its -5 so wouldnt you add it to both sides.

Answer 10

you have \[2 \sqrt{u} \ge 0\]

you are trying to find out what the inequality says about \[2 \sqrt{u}-5\]

Answer 11

so you need to subtract 5 on both sides of that inequality I have above

Answer 12

but -5 - 5 isnt 0

Answer 13

-5-5 is -10
but why are you doing that calculaution

Answer 14

I'm trying to get you to subtract 5 on both sides of the inequality
\[2 \sqrt{u} \ge 0\]

Answer 15

but it would be \[2\sqrt{x}-5 \ge 0 \] correct?

Answer 16

why aren't you will to do what I ask ?

Answer 17

\[2 \sqrt{u} \ge 0 \\ \text{ subtract 5 on both sides } \\ 2 \sqrt{u}-5 \ge 0-5 \\ 2 \sqrt{u}-5 \ge -5\]

Answer 18

what does this say about the range of 2 sqrt(u)-5 ?

Answer 19

it will be greater than or equal to -5

Answer 20

yes

Answer 21

2 sqrt(u)-5>=-5
says the lowest number in the range is -5
and anything greater than that is also in the range
so the range is [-5,inf)

Answer 22

SO if you had \[2 \sqrt{3x-4}+5 \\ \text{ you know the range of } 2 \sqrt{3x-4} \text{ is } [0,\infty) \\ \text{ that is you can write } 2 \sqrt{3x-4} \ge 0 \\ \text{ so adding 5 on both sides of your inequality } \\ 2 \sqrt{3x-4}+5 \ge 5 \\ \text{ tells you the range of } 2 \sqrt{3x-4}+5 \text{ is } [5,\infty)\]

Answer 23

\[\text{ if you had } -2 \sqrt{3x-4}+5 \text{ this will be a little different } \\ \sqrt{3x-4} \ge 0 \\ \text{ multiplying -2 on both sides gives } \\ -2 \sqrt{3x-4} \le 0 \text{ note: multiplying or dividing both sides of inequality } \\ \text{ changes direction of inequality } \\ \\ \text{ now adding 5 on both sides gives } -2 \sqrt{3x-4}+5 \le 5\]

Answer 24

do you know what this says about the range of
\[-2 \sqrt{3x-4}+5 ?\]

Answer 25

gosh my thingy got editted out accidentally

Answer 26

multiplying or dividing both sides of an inequality by a negative number changes the direction of the inequality