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Kunci Jawaban dan Pembahasan Soal || Buku Calculus 9th Purcell Chapter 0 - 0.4 Number 1 – 21

Pembahasan Soal Buku Calculus 9th Purcell Chapter 0 Section 0.4

◀ CHAPTER 0 PRELIMINARIES ▶

◀ SECTION 0.4 Graphs of Equations ▶


Problem Set 0.4, Number 1 – 21.
In Problems 1–30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all x- and y-intercepts.
  1. y = –x2 + 1
    2. 💬 SOLUTION:
    y = –x2 + 1; y-intercept = 1; y = (1 + x)(1 – x); x-intercepts = –1, 1.
    Symmetric with respect to the y-axis.
    Number 1
    ■

  2. x = –y2 + 1
    3. 💬 SOLUTION:
    x = –y2 + 1; y-intercepts = –1, 1; x-intercept = 1.
    Symmetric with respect to the x-axis.
    Number 2
    ■

  3. x = –4y2 – 1
    4. 💬 SOLUTION:
    x = –4y2 – 1; x-intercept = –1.
    Symmetric with respect to the x-axis.
    Number 3
    ■

  4. y = 4x2 – 1
    5. 💬 SOLUTION:
    y = 4x2 – 1; y-intercept = –1; y = (2x + 1)(2x – 1); x-intercepts = –1/2 , 1/2
    Symmetric with respect to the y-axis.
    Number 4
    ■

  5. x2 + y = 0
    6. 💬 SOLUTION:
    x2 + y = 0; y = –x2; x-intercept = 0, y-intercept = 0
    Symmetric with respect to the y-axis.
    Number 5
    ■

  6. y = x2 – 2x
    7. 💬 SOLUTION:
    y = x2 – 2x; y-intercept = 0; y = x(2 – x); x-intercepts = 0, 2
    Number 6
    ■

  7. 7x2 + 3y = 0
    8. 💬 SOLUTION:
    7x2 + 3y = 0; 3y = –7x2; y = –7/3x2; x-intercept = 0, y-intercept = 0.
    Symmetric with respect to the y-axis.
    Number 7
    ■

    Semoga Bermanfaat 😁

  8. y = 3x2 – 2x + 2
    9. 💬 SOLUTION:
    y = 3x2 – 2x + 2; y-intercept = 2.
    Number 8
    ■

  9. x2 + y2 = 4
    10. 💬 SOLUTION:
    x2 + y2 = 4; x-intercepts = –2, 2; y-intercepts = –2, 2.
    Symmetric with respect to the x-axis, y-axis, and origin.
    Number 9
    ■

  10. 3x2 + 4y2 = 12
    11. 💬 SOLUTION:
    3x2 + 4y2 = 12; y-intercepts = –√3, √3; x-intercepts = –2, 2.
    Symmetric with respect to the x-axis, y-axis, and origin.
    Number 10
    ■

  11. y = –x2 – 2x + 2
    12. 💬 SOLUTION:
    y = –x2 –2x + 2; y-intercept = 2; x-intercepts = 2±√(4+8)/–2 = 2±2√3/–2 = –1±√3.
    Number 11
    ■

  12. 4x2 + 3y2 = 12
    13. 💬 SOLUTION:
    4x2 + 3y2 = 12; y-intercepts = –2, 2; x-intercepts = –√3, √3.
    Symmetric with respect to the x-axis, y-axis, and origin.
    Number 12
    ■

  13. x2 – y2 = 4
    14. 💬 SOLUTION:
    x2 – y2 = 4; x-intercepts = –2, 2.
    Symmetric with respect to the x-axis, y-axis, and origin.
    Number 13
    ■

  14. x2 + (y – 1)2 = 9
    15. 💬 SOLUTION:
    x2 + (y – 1)2 = 9; y-intercepts = –2, 4; x-intercepts = –2√2, 2√2.
    Symmetric with respect to the y-axis.
    Number 14
    ■

    Semoga Bermanfaat 😁

  15. 4(x – 1)2 + y2 = 36
    16. 💬 SOLUTION:
    4(x – 1)2 + y2 = 36; y-intercepts = ±√32 = ±4√2; x-intercepts = –2, 4.
    Symmetric with respect to the x-axis.
    Number 15
    ■

  16. x2 – 4x + 3y2 = –2
    17. 💬 SOLUTION:
    x2 – 4x + 3y2 = –2; x-intercepts = 2±√2.
    Symmetric with respect to the x-axis.
    Number 16
    ■

  17. x2 + 9(y + 2)2 = 36
    18. 💬 SOLUTION:
    x2 + 9(y + 2)2 = 36; y-intercepts = –4, 0; x-intercept = 0.
    Symmetric with respect to the y-axis.
    Number 17
    ■

  18. x4 + y4 = 1
    19. 💬 SOLUTION:
    x4 + y4 = 1; y-intercepts = –1, 1; x-intercepts = –1, 1.
    Symmetric with respect to the x-axis, y-axis, and origin.
    Number 18
    ■

  19. x4 + y4 = 16
    20. 💬 SOLUTION:
    x4 + y4 = 16; y-intercepts = –2, 2; x-intercepts = –2, 2.
    Symmetric with respect to the y-axis, x-axis and origin.
    Number 19
    ■

  20. y = x3 – x
    21. 💬 SOLUTION:
    y = x3 – x; y-intercept = 0; y = x(x2 – 1) = x(x + 1)(x – 1); x-intercepts = –1, 0, 1.
    Symmetric with respect to the origin.
    Number 20
    ■

  21. y = 1/x2 + 1
    22. 💬 SOLUTION:
    y = 1/x2 + 1 ; y-intercept = 1.
    Symmetric with respect to the y-axis.
    Number 21
    ■

Semoga Bermanfaat 😁

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