# How do you find domain and range for #y= x^2-2#?

##### 2 Answers

#### Explanation:

#" y is well defined for all real values of x"#

#"domain is "x inRR#

#(-oo,oo)larrcolor(blue)"in interval notation"#

#"a quadratic in the form "y=x^2+c#

#"has a minimum turning point at "(0,c)#

#y=x^2-2" has a minimum turning point at "(0,-2)#

#"range is "y in[-2,oo)#

graph{x^2-2 [-10, 10, -5, 5]}

Domain:

Range:

#### Explanation:

**DOMAIN**

This function is a polynomial, which means that it is a sum of powers of

This means that, for every input

- compute the powers
#x# ,#x^2# , ...,#x^n# . This can be done with no restrictions on#x# . - Multiply each power for its coefficient:

#x\to a_1x# ,

#x^2\toa_2x^2# ,

..

#x^n\to a_nx^n# .

Again, this can be done for every input. - Finally, you have to sum all this pieces, and you can always sum a finite number of terms.

This proves that the domain of **every** polynomial is the whole set of real numbers

**RANGE**

Since this is a polynomial of degree

This means that the parabola has a point of minimum, but it has no upper bound. Its range is thus something like

To find the minimum, we can either derive the parabola, or use the formula for the vertex: given a parabola

In your case,

The minimum is thus the image of

So, the range is