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Mathematics LibreTexts

2.5E: Absolute Value Functions (Exercises)

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  • Page ID
    13901
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    Write an equation for each transformation of \(f(x)=|x|\)

    1.image 2.image

    3.image 4.image

    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 \[21. |\; x+5\; |<6 22. |\; x-3\; |<7\] \[23. |\; x-2\; |\ge 3 24. |\; x+4\; |\ge 2\] \[25. |\; 3x+9\; |<4 26. |\; 2x-9\; |\le 8\]