2.5E: Absolute Value Functions (Exercises)
- Page ID
- 13901
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)section 2.5 exercise
Write an equation for each transformation of \(f(x)=|x|\)
1.
2.
3. 
4.
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.
7.
9.
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 \((-\dfrac{13}{3}, -\dfrac{5}{3})\)