Mathematics 10 — Exercise 4.2 · Q1 (vi)

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.

   $$x+1=0$$

2. Equate the corresponding entries.

   $$x+1=0$$

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

   $$x=0-1$$

4. Simplify the constant calculation.

   $$x=-1$$

5. Divide both sides by the variable coefficient.

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

6. Reduce the fraction.

   $$x=-1$$

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

   $$-6=-6$$

8. Calculate this operation before combining the remaining terms.

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

9. Calculate this operation before combining the remaining terms.

   $$-4+1=-3$$

10. Substitute this x into the inside expression.

    $$1\times \left(-4.0\right)+1=-3.0$$

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

    $$-6+2\times \left|1-4.0\right|=0$$

12. Calculate this operation before combining the remaining terms.

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

13. Calculate this operation before combining the remaining terms.

    $$-3+1=-2$$

14. Substitute this x into the inside expression.

    $$1\times \left(-3.0\right)+1=-2.0$$

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

    $$-6+2\times \left|1-3.0\right|=-2.0$$

16. Calculate this operation before combining the remaining terms.

    $$1\times \left(-2\right)=-2$$

17. Calculate this operation before combining the remaining terms.

    $$-2+1=-1$$

18. Substitute this x into the inside expression.

    $$1\times \left(-2.0\right)+1=-1.0$$

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

    $$-6+2\times \left|1-2.0\right|=-4.0$$

20. Calculate this operation before combining the remaining terms.

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

21. Calculate this operation before combining the remaining terms.

    $$-1+1=0$$

22. Substitute this x into the inside expression.

    $$1\times \left(-1.0\right)+1=0.0$$

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

    $$-6+2\times \left|1-1.0\right|=-6$$

24. Calculate this operation before combining the remaining terms.

    $$1\times 0=0$$

25. Calculate this operation before combining the remaining terms.

    $$0+1=1$$

26. Substitute this x into the inside expression.

    $$1\times 0.0+1=1.0$$

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

    $$-6+2\times \left|1+0.0\right|=-4.0$$

28. Calculate this operation before combining the remaining terms.

    $$1\times 1=1$$

29. Calculate this operation before combining the remaining terms.

    $$1+1=2$$

30. Substitute this x into the inside expression.

    $$1\times 1.0+1=2.0$$

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

    $$-6+2\times \left|1+1.0\right|=-2.0$$

32. Calculate this operation before combining the remaining terms.

    $$1\times 2=2$$

33. Calculate this operation before combining the remaining terms.

    $$2+1=3$$

34. Substitute this x into the inside expression.

    $$1\times 2.0+1=3.0$$

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

    $$-6+2\times \left|1+2.0\right|=0$$

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.