Graph the function. Then state the domain and range.

Question

Graph the function. Then state the domain and range.

 

1.  y = 2√x

 

2.  y = -3 ³√x          <-- I mean cube root of x

 

3.  y = 2√x+2  -2

 

4.  y = 1/2 ³√x+3  -1        <-- I mean cube root of x+3

 

I do not know what it means to state the domain and range... Please help I would really appreciate it. Thank you very much! :)

Answer 1

1)

 

To find the domain,

 

set x≥0.

 

 

Domain is [0, ∞)

 

To find the range evaluate the function using the domain.

 

y = 2√0 = 0

y = 2√1 = 2

y = 2√4 = 4

This continues forever.

 

Range is [0, ∞).

 

 

2)

 

In an odd root, the domain is all real numbers.  That is because raising a negative number to an odd power is negative, and raising a positive number to an odd power is positive.  It has not restrictions.  Knowing that, what is the range of the function?  Well, lets pick a large negative number and large positive number as x.   We will use these values of x to evaluate y.  We should also evaluate when x=0.  At this value of x, y=0.

 

y = -3 * ³√(-216) = -3 * -6 = 18

y = -3 * ³√(216) = -3 * 6 = -18

 

If we decrease x from -216 and increase x from 216, y will increase from 18 and y will decrease from -18.  Do you see the pattern.

 

The range is all real numbers (-∞, ∞).

 

 

Note that problem 4 has the same situation here.

 

Try problems 3 and 4 on your own using the same procedure.