Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

2.5E: Absolute Value Functions (Exercises)

  • Page ID
    13901
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    section 2.5 exercise

    Write an equation for each transformation of \(f(x)=|x|\)

    1.屏幕快照 2019-06-21 下午8.02.21.png 2.屏幕快照 2019-06-21 下午8.02.52.png

    3. 屏幕快照 2019-06-21 下午8.03.11.png4.屏幕快照 2019-06-21 下午8.03.33.png

    Sketch a graph of each function

    5. \(f(x) = -|x-1|-1\)

    6. \(f(x)= -|x+3|+4\)

    7. \(f(x)= 2|x+3|+1\)

    8. \(f(x)=3|x-2|-3\)

    9. \(f(x)=|2x-4|-3\)

    10. \(f(x)=|3x+9|+2\)

    Solve each the equation

    11. \(|5x-2|=11\)

    12. \(|4x+2|=15\)

    13. \(2|4-x|=7\)

    14. \(3|5-x|=5\)

    15. \(3|x+1|-4=-2\)

    16. \(5|x-4|-7=2\)

    Find the horizontal and vertical intercepts of each function

    17. \(f(x)= 2|x+1|-10\)

    18. \(f(x)= 4|x-3|+4\)

    19. \(f(x)=-3|x-2|-1\)

    20. \(f(x)= -2|x+1|+6\)

    Solve each inequality

    21. \(| x+5 |<6\)

    22. \(| x-3 |<7\)

    23. \(| x-2 |\ge 3\)

    24. \(| x+4 |\ge 2\)

    25. \(| 3x+9 |<4\)

    26. \(| 2x-9 |\le 8\)

    Answer

    1. \(y = \dfrac{1}{2}|x + 2| + 1\)

    3. \(y = -3|x - 3| + 3\)

    5. Screen Shot 2019-10-01 at 8.28.41 PM.png

    7. Screen Shot 2019-10-01 at 8.29.06 PM.png

    9. Screen Shot 2019-10-01 at 8.29.25 PM.png

    11. \(x = -\dfrac{9}{5}\) or \(x = \dfrac{13}{5}\)

    13. \(x = \dfrac{1}{2}\) or \(x = \dfrac{15}{2}\)

    15. \(x = -\dfrac{5}{3}\) or \(x = -\dfrac{1}{3}\)

      Horizontal Intercepts  Vertical Intercept
    17. (-6, 0) and (4, 0) (0, -8)
    19.  none (0, -7)

    21. \(-11 < x < 1\) or (-11, 1)

    23. \(x \ge 5\), \(x \le -1\) or \((-\infty, -1] \cup [5, \infty)\)

    25. \(-\dfrac{13}{3} < x < -\dfrac{5}{3}\) or \((-\dfrac{13}{3}, -\dfrac{5}{3})\)