Question

i need help finding the domain and range

Answer 1

Since there is a square root of x involved, what numbers can you take the square root of?

Answer 2

all real numbers but not negatives?

Answer 3

Right. You can say: non-negative numbers.
In other words, x can be zero or positive.

Answer 4

The doamin is: \(x \ge 0\)

Answer 5

Ok so far?

Answer 6

yea

Answer 7

Now we need to deal with the range.

Answer 8

The smallest x is zero.
If you have x = 0, \(8\sqrt{0} = 0\), so that gives you the smallest value y can have since the function is \(y = 8\sqrt{x} - 14\)
\(f(0) = 8\sqrt{0} - 14 = -14\)

Answer 9

ok

Answer 10

For any value of x greater than zero, the square root will be greater than 0 and the value of y will be larger and larger as x increases.

Answer 11

That means the smallest y can be is -14, but there is no upper bound. y increases to infinity as x increases to infinity.

Answer 12

That gives us the range: \(y \ge -14\)

Answer 13

[-14,infinity) ??

Answer 14

Correct for range.

Answer 15

so in general when i am trying to find the range i would need to find the domain first to plug in the smallest number x can be to find the smallest number y can be for the range?

Answer 16

\(\bf \large D:~[0, \infty)\)
\(\bf \large R:~[-14, \infty)\)

Answer 17

It is definitely helpful to look at the domain to see what values of x can be used. Sometimes, there is a maximum value of x that can give you a maximum or minimum y value. You need to look at the things that are happening to x that constrain its domain: x in the denominator, x in radicals, log of x, etc.

Answer 18

oh ok thank you very much

Answer 19

You are welcome.