Mathematics 10 — Exercise Review · Q5 (ii)

Full question

Construct a table of values for the following function and use it to draw the graph on a coordinate plane.

Step-by-step solution

1. The vertex occurs where the expression inside the absolute value is zero.

   $$x+6=0$$

2. Equate the corresponding entries.

   $$x+6=0$$

3. Collect the variable terms on the left and constants on the right.

   $$x=0-6$$

4. Simplify the constant calculation.

   $$x=-6$$

5. Divide both sides by the variable coefficient.

   $$x=-6\times \frac{1}{1}$$

6. Reduce the fraction.

   $$x=-6$$

7. Substitute the vertex input; |0| = 0, leaving the vertical shift.

   $$-2=-2$$

8. Calculate this operation before combining the remaining terms.

   $$1\times \left(-9\right)=-9$$

9. Calculate this operation before combining the remaining terms.

   $$-9+6=-3$$

10. Substitute this x into the inside expression.

    $$1\times \left(-9.0\right)+6=-3.0$$

11. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-9.0\right|=1.0$$

12. Calculate this operation before combining the remaining terms.

    $$1\times \left(-8\right)=-8$$

13. Calculate this operation before combining the remaining terms.

    $$-8+6=-2$$

14. Substitute this x into the inside expression.

    $$1\times \left(-8.0\right)+6=-2.0$$

15. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-8.0\right|=0$$

16. Calculate this operation before combining the remaining terms.

    $$1\times \left(-7\right)=-7$$

17. Calculate this operation before combining the remaining terms.

    $$-7+6=-1$$

18. Substitute this x into the inside expression.

    $$1\times \left(-7.0\right)+6=-1.0$$

19. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-7.0\right|=-1.0$$

20. Calculate this operation before combining the remaining terms.

    $$1\times \left(-6\right)=-6$$

21. Calculate this operation before combining the remaining terms.

    $$-6+6=0$$

22. Substitute this x into the inside expression.

    $$1\times \left(-6.0\right)+6=0.0$$

23. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-6.0\right|=-2$$

24. Calculate this operation before combining the remaining terms.

    $$1\times \left(-5\right)=-5$$

25. Calculate this operation before combining the remaining terms.

    $$-5+6=1$$

26. Substitute this x into the inside expression.

    $$1\times \left(-5.0\right)+6=1.0$$

27. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-5.0\right|=-1.0$$

28. Calculate this operation before combining the remaining terms.

    $$1\times \left(-4\right)=-4$$

29. Calculate this operation before combining the remaining terms.

    $$-4+6=2$$

30. Substitute this x into the inside expression.

    $$1\times \left(-4.0\right)+6=2.0$$

31. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-4.0\right|=0$$

32. Calculate this operation before combining the remaining terms.

    $$1\times \left(-3\right)=-3$$

33. Calculate this operation before combining the remaining terms.

    $$-3+6=3$$

34. Substitute this x into the inside expression.

    $$1\times \left(-3.0\right)+6=3.0$$

35. Take its absolute value, multiply by the outside factor, then add the shift.

    $$-2+\left|6-3.0\right|=1.0$$

36. Plot the table points and join them with the two straight arms of the V-shaped graph.

Answer

The final answer is shown below.