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Algebra 1 Name___________________________________ Functions, Domain, and Range Review Date________________ Block____ ©T m2o0U1B4y xKYuitqa3 BSZoNfatBwya4rSeD 0LxLxCT.u g zAHlGlQ Frti6gfhvtqs5 KrTeYs5edruvUeCdJ.w 1) When is a relation a function? What are some ways to tell if a relation is a function? 2) What is the domain of a function? What is the range of a function? Given a member of the domain, how do you find its value in the range? If f ( x) = −4 x − 7, find... If f ( x) = −3 x − 2 x + 1, find... 3) a) f (3) 4) a) f (−4) 2 b) f (−7) b) f (0) For each question, decide if it is a function. Then find the domain and range in set builder notation. 5) 6) y −8 −6 −4 8 6 6 4 4 2 2 −2 2 4 6 8 x −4 −6 −4 −2 −2 −4 −4 −6 −6 −8 −8 8) y −6 −8 −2 7) −8 y 8 8 6 6 4 4 2 2 2 4 6 8 x 4 6 8 x 2 4 6 8 x y 8 −2 2 −8 −6 −4 −2 −2 −2 −4 −4 −6 −6 −8 −8 Given the function and a domain, find the range. 9) f ( x) = −7 x + 3, D={-12, -4, 3, 20} 10) f ( x) = 2 x − 2 x + 5, D={-2, -1, 0, 1, 2} 11) f ( x) = 4 x − 1, D={ x| x} 12) f ( x) = 2 x 2 − 6 x + 11, D={ x| x} ©p c2y0A1B4o PKmugtsaF aSRoQfItqw1aRrre1 WLZLGCU.M K kAElblL Urbijg4hetWsl SrTeosxemrHvQeLdX.V O 7MWahdveQ kwaibtEhs IIhnSfUiMnQiltKeA pAGlYgAeAbjr2az 91U.O 2 Worksheet by Kuta Software LLC For each question, decide if it is a function. Then find the domain and range in set builder notation. 13) 14) y −8 −6 −4 8 6 6 4 4 2 2 −2 2 4 6 8 x −4 −6 −4 −2 −2 −4 −4 −6 −6 −8 −8 16) y −6 −8 −2 15) −8 y 8 8 6 6 4 4 2 2 2 4 6 8 x 4 6 8 x 2 4 6 8 x y 8 −2 2 −8 −6 −4 −2 −2 −2 −4 −4 −6 −6 −8 −8 If f ( x) = −3 x − 2, find... If f ( x) = −11 x − 5 x + 13, 13 find... 17) a) f (0) b) f (4) c) f (−1) 18) a) f (1) b) f (−1) c) f (−4) 2 Given the function and a domain, find the range. 19) f ( x) = −6 x − 1; D={-2, -1, 0, 5} 20) f ( x) = −3 x 2 + x + 8; D={-2, -1, 0, 1} 21) f ( x) = 2 x 2 + 8 x + 3; D={ x| x} 22) f ( x) = −4 x 2 + 8 x + 3; D={ x| x} ©0 S2r0l1D4u WKduutzab gS1ocfhtFwaaWrVeE zLzLKCZ.2 U TAWlwlh JrHiYgShmtFs2 arkeHsmeHrTvVe9dk.Q h SMGaeduep ZwOiLt6h7 FIqn1fOitnLiytve2 NAFlkgueMbNrDad 41a.W Worksheet by Kuta Software LLC Answers to Functions, Domain, and Range Review 1) Every input has OAOO output; find an x with more than one y / vertical line test 2) Set of inputs; set of outputs; set x to the domain value and calculate y 3) a) -19 b) 21 4) a) -39 b) 1 5) yes; All real numbers for both: D={ x| x}, R={ y| y} 6) yes; D={ x| x}, R={ y| y ≥ −4} 7) not a function; D={ x| x ≥ −3}, R={ y| y} 8) not a function; D={ x|−2 ≤ x ≤ 6}, R={ y|−6 ≤ y ≤ 2} 9) R={87, 31, -18, -137} 10) R={17, 9, 5} 11) R={ y| y} 12) R={ y| y ≥ 2} 13) yes; D={ x|x}, R={ y|y=-2} 14) no; D={−3}, R={-4, 0, 4} 15) yes; D={ x| x}, R={ y| y} 16) no; D={ x|−5 ≤ x < 5}, R={ y|−2 ≤ y ≤ 2} 17) a) -2 b) -14 c) 1 18) a) -3 b) 7 c) -143 19) R={11, 5, -1, -31} 20) R={-6, 4, 8, 6} 21) R={ y| y ≥ −5} 22) R={ y| y ≤ 7} ©2 a2K0Y1i4f sKXuKtmaR TSAorfZt7wearrue5 3LdLdCT.f 0 hAvlplc 4r4irgLh6tns4 9rbeHsseer7vkewd2.r k nMPagdTeh SwViptBhE 2IknXfoiTnSibtfe3 mAnlpgteEbTr3aq U1C.M Worksheet by Kuta Software LLC