1. Domain & Range
Unit 8

2. Avoid 𝑥 0 −𝑥 How to find the Domain
Look for those values of the independent variable (usually x) which we are allowed to use.
Usually we have to avoid 0 on the bottom of a fraction or
Negative values under the square root sign
𝑥 0
Avoid −𝑥

3. How to find the Range
The range is the resulting y-values we get after substituting all the possible x-values.
The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)
Make sure you look for minimum and maximum values of y.
Draw a sketch! In math, it's very true that a picture is worth a thousand words.

4. f(x)=x​2​​+2 Domain: “all real numbers of x” Range: “all real numbers of y ≥2

5. 𝑔 𝑠 = 3−𝑠 Domain: ”all real numbers ≤3” Range: “all real numbers ≥0”

6. Let’s Practice The range is "all y ≤ 4".
The graph goes only as high as y = 4, but it will go as low as I like.
The range is "all y ≤ 4".
There are no denominators (so no division-by-zero problems) and no radicals (so no square-root-of-a-negative problems).
There are no problems with a polynomial.
There are no values that I can't plug in for x.
When I have a polynomial, the answer for the domain is always “all x”.

7. For extra practice go to CoolMath.com