SOLUTIONS MANUAL TO PRECALCULUS AN INVESTIGATION OF FUNCTIONS DAVID LIPPMAN, MELONIE RASMUSSEN 1ST EDITION SHORELINE COMMUNITY COLLEGE THE EVERGREEN STATE COLLEGE EDITED BY ROSALIE TEPPER LATEST UPDATE.

SOLUTIONS MANUAL TO


PRECALCULUS
AN INVESTIGATION OF FUNCTIONS
DAVID LIPPMAN, MELONIE
RASMUSSEN 1ST EDITION




SHORELINE COMMUNITY
COLLEGE THE EVERGREEN
STATE COLLEGE EDITED BY
ROSALIE TEPPER LATEST
UPDATE.

,THIS SOLUTIONS MANUAL WAS PREPARED BY STUDENT TUTORS AT SHORELINE COMMUNITY COLLEGE
AND THE EVERGREEN STATE COLLEGE, AND WAS EDITED BY ROSALIE TEPPER.

CONTRIBUTORS INCLUDE: KATIE GATES, MAGGIE ARBEENY, SOREN WELLMAN, MADELEINE BEATTY,
EDWARD LILLEY, KALYANI LOGANATHAN, MATT GROVE, JOHN LEWIS, GEORGE MARSH, BEINUO GONG,
MYHUONG CAO, TRENT LINSON, KAITLYN FRANZ, AND LUCAS KRAFT.

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,1.1 SOLUTIONS TO EXERCISES
1. (A) 𝑓(40) = 13, BECAUSE THE INPUT 40 (IN THOUSANDS OF PEOPLE) GIVES THE
OUTPUT 13 (IN TONS OF GARBAGE)
(B) 𝑓(5) = 2, MEANS THAT 5000 PEOPLE PRODUCE 2 TONS OF GARBAGE PER WEEK.
3. (A) IN 1995 (5 YEARS AFTER 1990) THERE WERE 30 DUCKS IN THE LAKE.
(b) IN 2000 (10 YEARS AFTER 1990) THERE WERE 40 DUCKS IN THE LAKE.

5. GRAPHS (A) (B) (D) AND (E) REPRESENT Y AS A FUNCTION OF X BECAUSE FOR
EVERY VALUE OF X THERE IS ONLY ONE VALUE FOR Y. GRAPHS (C) AND (F) ARE
NOT FUNCTIONS BECAUSE THEY CONTAIN POINTS THAT HAVE MORE THAN ONE
OUTPUT FOR A GIVEN INPUT, OR VALUES FOR X THAT HAVE 2 OR MORE VALUES
FOR Y.

7. TABLES (A) AND (B) REPRESENT Y AS A FUNCTION OF X BECAUSE FOR EVERY
VALUE OF X THERE IS ONLY ONE VALUE FOR Y. TABLE (C) IS NOT A FUNCTION
BECAUSE FOR THE INPUT X=10, THERE ARE TWO DIFFERENT OUTPUTS FOR Y.

9. TABLES (A) (B) AND (D) REPRESENT Y AS A FUNCTION OF X BECAUSE FOR
EVERY VALUE OF X THERE IS ONLY ONE VALUE FOR Y. TABLE (C) IS NOT A
FUNCTION BECAUSE FOR THE INPUT X=3, THERE ARE TWO DIFFERENT OUTPUTS
FOR Y.

11. TABLE (B) REPRESENTS Y AS A FUNCTION OF X AND IS ONE-TO-ONE BECAUSE
THERE IS A UNIQUE OUTPUT FOR EVERY INPUT, AND A UNIQUE INPUT FOR
EVERY OUTPUT. TABLE (A) IS NOT ONE-TO-ONE BECAUSE TWO DIFFERENT
INPUTS GIVE THE SAME OUTPUT, AND TABLE (C) IS NOT A FUNCTION BECAUSE
THERE ARE TWO DIFFERENT OUTPUTS FOR THE SAME INPUT X=8.

13. GRAPHS (B) (C) (E) AND (F) ARE ONE-TO-ONE FUNCTIONS BECAUSE THERE IS A
UNIQUE INPUT FOR EVERY OUTPUT. GRAPH (A) IS NOT A FUNCTION, AND GRAPH
(D) IS NOT ONE-TO-ONE BECAUSE IT CONTAINS POINTS WHICH HAVE THE SAME
OUTPUT FOR TWO DIFFERENT INPUTS.

15. (A) 𝑓(1) = 1 (B) 𝑓(3) = 1

17. (A) 𝑔(2) = 4 (B) 𝑔(−3) = 2

19. (A) 𝑓(3) = 53 (B) 𝑓(2) = 1

21. 𝑓(−2) = 4 − 2(−2) = 4 + 4 = 8, 𝑓(−1) = 6, 𝑓(0) = 4, 𝑓(1) = 4 − 2(1) = 4 − 2 =
2, 𝑓(2) = 0

, THIS MATERIAL WAS CREATED BY SHORELINE COMMUNITY COLLEGE AND THE EVERGREEN STATE COLLEGE, AND
EDITED BY ROSALIE TEPPER. THIS MATERIAL IS LICENSED UNDER A CREATIVE COMMONS NONCOMMERCIAL-
SHAREALIKE LICENSE.