
# 2.5E: Absolute Value Functions (Exercises)

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

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

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

1. 2.

3. 4.

Sketch a graph of each function $5. f(x)\; =\; -|x-1|-1 6. f\left(x\right)=\; -\left|x+3\right|+4$ $7. f\left(x\right)=\; 2\left|x+3\right|+1 8. f\left(x\right)=3\left|x-2\right|-3$ $9. f\left(x\right)=\left|2x-4\right|-3 10. f\left(x\right)=\left|3x+9\right|+2$

Solve each the equation $11. |5x-2|=11\; 12. |4x+2|=15 13. 2|4-x|=7\; 14. 3|5-x|=5$ $15. 3\left|x+1\right|-4=-2\; 16. 5\left|x-4\right|-7=2$

Find the horizontal and vertical intercepts of each function $17. f(x)=\; 2|x+1|-10 18. f\left(x\right)=\; 4\left|x-3\right|+4$ 19. $$f\left(x\right)=-3\left|x-2\right|-1$$ 20. $$f\left(x\right)=\; -2\left|x+1\right|+6$$Solve each inequality $21. |\; x+5\; |<6 22. |\; x-3\; |<7$ $23. |\; x-2\; |\ge 3 24. |\; x+4\; |\ge 2$ $25. |\; 3x+9\; |<4 26. |\; 2x-9\; |\le 8$