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D domain and-range

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D domain and-range

1. 1. 2 xy = ( ) 8]73[ 2 −−= xy x y 1 = xy = 7)(5 −= xfy xy 3= 86 += xy Function FormulaFunction NotationFunction )]1(2[4 +−−= xfy 8)]7(3[ −−= xfy 1 2 + = x y 8)2( += xfy 75 −= xy
2. 2. 1.4 – Domain & Range
3. 3. Domain: Range: - the x-values of a relation - the y-values of a relation Determine the domain and range of the relations on the following pages. Determine the domain and range of the relations on the following pages.
4. 4. Domain = {x∈R} Range = {y∈R} ‘x’ belongs to the set of real numbers ‘x’ belongs to the set of real numbers
5. 5. Domain = {x∈R} Range = {y∈R|y≤6} ‘y’ is less than or equal to 6 ‘y’ is less than or equal to 6
6. 6. {(2,4), (3,5), (4,6), (5,7)} Domain = {2,3,4,5} Range = {4,5,6,7}
7. 7. Domain = {x∈R|-3<x≤5} Range = {y=3} ‘x’ is greater than -3, but less than or equal to 5 ‘x’ is greater than -3, but less than or equal to 5
8. 8. Domain = {x∈R|-4≤x≤4} Range = {y∈R |-4≤y≤4}
9. 9. Domain = {x∈Ι|-6≤x≤3} Range = {y∈Ι |-1≤y≤8} ‘x’ belongs to the set of integers ‘x’ belongs to the set of integers
10. 10. What about equations? 8)1(2)( 2 −−= xxg 53)( −= xxfa) b) This is a linear function (not and not vertical or horizontal), so x and y can be any value. Domain = {x∈R}Domain = {x∈R} Range = {y∈R}Range = {y∈R} • This is a quadratic function. • It opens upward, thus has a min. • The min. value is -8. Domain = {x∈R}Domain = {x∈R} Range = {y∈R|y≥-8}Range = {y∈R|y≥-8}
11. 11. 9)( += xxhc) Are there any restrictions that must be placed on ‘x’, or will any ‘x’ value work in this function? Are there any restrictions that must be placed on ‘x’, or will any ‘x’ value work in this function?Can’tbe-’ve So, what values of ‘x’ will not make the part under the squareroot sign negative? Domain = {x∈R|x≥-9}Domain = {x∈R|x≥-9} Range = {y∈R|y≥0}Range = {y∈R|y≥0}