Domain & Range Unit 8
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
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.
f(x)=x2+2 Domain: “all real numbers of x” Range: “all real numbers of y ≥2
𝑔 𝑠 = 3−𝑠 Domain: ”all real numbers ≤3” Range: “all real numbers ≥0”
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”.
For extra practice go to CoolMath.com