2.5E: Absolute Value Functions (Exercises)

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Jan 2, 2021
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- 2.5: Absolute Value Functions
- 3: Polynomial and Rational Functions.

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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. $屏幕快照 2019-06-21 下午8.03.11.png$ 4. $屏幕快照 2019-06-21 下午8.03.33.png$

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 $(-\dfrac{13}{3}, -\dfrac{5}{3})$

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