Thread: cubed root domain and range

1. cubed root domain and range

i have a cubed root funtion i cannot figure out if the domain and range are correct for.

y=(³√x)(x≤0)
y=(-³√x)(x√0)

i tried the domain and got this.
(-∞,0]
(-∞,0]

please help me find my range and let me know if my domain is correct, thank you

2. Originally Posted by paa13
i have a cubed root funtion i cannot figure out if the domain and range are correct for.

y=(³√x)(x≤0)
y=(-³√x)(x√0)

i tried the domain and got this.
(-∞,0]
(-∞,0]

please help me find my range and let me know if my domain is correct, thank you
Is this a hybrid function or two separate functions?

3. sorry, two seperate functions

4. Originally Posted by paa13
i have a cubed root funtion i cannot figure out if the domain and range are correct for.

y=(³√x)(x≤0)
y=(-³√x)(x√0)

i tried the domain and got this.
(-∞,0]
(-∞,0]

please help me find my range and let me know if my domain is correct, thank you
I assume the second should have a $\displaystyle \leq$ where the square root symbol is...

You're told what the domains are. The domain is the set of values x can take. So in both cases, the domain is $\displaystyle x\leq0$. What you've written in interval notation is also fine.

Remember that the cubed root of a number has the same sign as the original number itself. So the cube root of any negative number stays negative. That means that the range of the first is the same as the domain, i.e. $\displaystyle y \leq 0$.

The second function is a reflection in the x-axis of the first.

So the range of the second function is $\displaystyle y \geq 0$.

5. Originally Posted by Prove It
I assume the second should have a $\displaystyle \leq$ where the square root symbol is...

You're told what the domains are. The domain is the set of values x can take. So in both cases, the domain is $\displaystyle x\leq0$. What you've written in interval notation is also fine.

Remember that the cubed root of a number has the same sign as the original number itself. So the cube root of any negative number stays negative. That means that the range of the first is the same as the domain, i.e. $\displaystyle y \leq 0$.

The second function is a reflection in the x-axis of the first.

So the range of the second function is $\displaystyle y \geq 0$.
how is that in interval notation, 1.(- infin.,0] and then 2.[0, infin.)
do i have them in the wrong order?

6. Originally Posted by paa13
how is that in interval notation, 1.(- infin.,0] and then 2.[0, infin.)
do i have them in the wrong order?
$\displaystyle (-\infty, 0]$ and $\displaystyle [0, \infty)$ is correct.

7. ty soo much, yer a life saver