Question

Need help with domain and range!!

Answer 1

Find the domain and range of the function \[y=2\sqrt{3x+4-5}\]

Answer 2

Will fan!!

Answer 3

3x+4-5? is it correct?

Answer 4

@Harley-Quinn

Answer 5

that is under a Square root https://www.connexus.com/content/media/459431-3172011-84450-AM-1622409520.png

Answer 6

ok so 3x+4-5 >=0 implies 3x>=1 implies x>=1/3
so the domain is [1/3,infinity) and range is the set of all positive real numbers

Answer 7

Would that be
\[x \ge-\frac{ 4 }{ 3 } ;y \ge-5\]
\[x \ge \frac{ 4 }{ 3 };y \ge -5\]
\[x \le-\frac{ 4 }{ 3 };y \le-5\]
or \[x \ge-\frac{ 4 }{ 3 };y \ge5\]

Answer 8

@jango_IN_DTOWN

Answer 9

the term inside the square root is not correct..... you post the question properly..

Answer 10

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

Answer 11

looking at the solutions I think the problem is

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

Answer 12

yes

Answer 13

uhhhh I kept on telling you look at the questoin

Answer 14

its ok @campbell_st will help you,:)

Answer 15

ok... so the domain:

you can't that the square root of a negative number.... in terms or real numbers

so then the part inside the square your has to be greater than or equal to zero

so you need to solve

\[3x + 4 \ge 0\]

this will be the domain.

Now for the range

if the square root value is zero... what is the value of y...?

Answer 16

the range will basically be all values going up from the y- intercept...

hope that helps

Answer 17

i am not good with this at all sorry...

Answer 18

so you can't solve

\[3x + 4 \ge 0\]

could you solve

3x + 4 = 0.....?

Answer 19

i am not sure if it is just me but the bottom one makes more sense some how...
you would subtract 4 from both sides??

Answer 20

well the same steps will apply to the inequality

subtracting 4 is a good start

\[3x \ge -4 \]

now get a single x.... the answer will give the domain...

Answer 21

you would divide 3 so \[-\frac{ 4 }{ 3 }\]

Answer 22

great so you have the domain

\[x \ge -\frac{4}{3}\]

now the range, find the y- intercept...

let

\[\sqrt{x3x + 4} = 0\]

so the equation becomes

\[y = 0 - 5\]

where does the curve cut the y-axis..?

Answer 23

at -5??

Answer 24

great so that is the lowest part of the range... and then the values of y just keep increasing.

\[increasing~~~ \ge\]

so what answer do you think matches the domain and range..?

Answer 25

\[y \ge-5\] for range and \[x \ge-\frac{ 4 }{ 3 }\] for domain

Answer 26

great... so now you have the answer

Answer 27

Thank you <3

Answer 28

can you help me with one more?

Answer 29

@campbell_st