Name the quadrant or the axis on which the following points lie. Exercise Name the quadrant or the axis on which the following points lie.

(−3, −4)

(−2, 10)

(15, 0)

(0.5, 253)

(0, 0.5)

(0, 0)

Relation A relation is a set of ordered pairs.

Domain & Range A = {(2, 3), (−3, 2), (−4, −3), (4, −3)} Domain: D = {−4, −3, 2, 4} Range: R = {−3, 2, 3}

Example 1 Give the domain and range of the relation C. C = {(−1, 3), (2, 0), (2, 3), (3, −2), (−2, −4)}. D = {−2, −1, 2, 3}; R = {−4, −2, 0, 3}

Example Give the domain and range of the relation R = {(0, 1), (−3, 2), (5, 4), (2, −3)}. D = {−3, 0, 2, 5}; R = {−3, 1, 2, 4}

Example Give the domain and range of the graphed segment. D = −4 ≤ x ≤ 2; R = {3}

Example If the segment is changed to a line, what is the relation’s domain and range? D = real numbers; R = {3}

Example 2 Write the set of ordered pairs for the relation shown. Name the relation C.

y A B D x C F E

C = {(−2, 5), (−5, −2), (3, 2), (1, 6), (3, −6), (0, −5)}

Example 3 Write the set of ordered pairs for relation G if y = 2x for each ordered pair and the domain of the relation is {−2, 0, 1, 3}.

y = 2x x = −2 y = 2(−2) = −4 x = 0 y = 2(0) = 0 x = 1 y = 2(1) = 2 x = 3 y = 2(3) = 6 G = {(−2, −4), (0, 0), (1, 2), (3, 6)}

Example 4 Graph the relation G = {(−2, 3), (−4, −1), (0, 6), (3, 6), (5, 7)}.

y x

Example 5 Graph the relation J if y = x + 3 for each ordered pair and the domain of the relation is {−4, 0, 3}.

y = x + 3 x = −4 y = −4 + 3 = −1 x = 0 y = 0 + 3 = 3 x = 3 y = 3 + 3 = 6 J = {(−4, −1), (0, 3), (3, 6)}

y x

Example Graph the relation A = {(1, 2), (−2, 2), (3, 3), (−1, 3)} and give its domain and range. D = {−2, −1, 1, 3} R = {2, 3}

y x

Example Graph the relation B = {(1.5, 2.5), (2.25, 3.75), (4, 5)} and give its domain and range. D = {1.5, 2.25, 4} R = {2.5, 3.75, 5}

y x

Example Write the set of ordered pairs for relation C if y = 3x − 2 for each ordered pair and the domain of the relation is {−2, −1, 0, 1, 2}. C = {(−2, −8), ( −1, −5), (0, −2), (1, 1), (2, 4)}

Exercise Give the domain and range of the following relation, and determine the equation that describes each relation. {(1, −4), (2, −8), (3, −12), (4, −16)} D = {1, 2, 3, 4}; R = {−4, −8, −12, −16}; y = −4x

Exercise Give the domain and range of the following relation, and determine the equation that describes each relation. {(−9, −3), (−6, −2), (−3, −1), (0, 0)} D = {−9, −6, −3, 0}; R = {−3, −2, −1, 0}; y = ⅓x