Mathematics 10 — Exercise 4.2 · Q1 (v)

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.

   $$x+4=0$$

2. Equate the corresponding entries.

   $$x+4=0$$

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

   $$x=0-4$$

4. Simplify the constant calculation.

   $$x=-4$$

5. Divide both sides by the variable coefficient.

   $$x=-4\times \frac{1}{1}$$

6. Reduce the fraction.

   $$x=-4$$

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

   $$-3=-3$$

8. Calculate this operation before combining the remaining terms.

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

9. Calculate this operation before combining the remaining terms.

   $$-7+4=-3$$

10. Substitute this x into the inside expression.

    $$1\times \left(-7.0\right)+4=-3.0$$

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

    $$-3+2\times \left|4-7.0\right|=3.0$$

12. Calculate this operation before combining the remaining terms.

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

13. Calculate this operation before combining the remaining terms.

    $$-6+4=-2$$

14. Substitute this x into the inside expression.

    $$1\times \left(-6.0\right)+4=-2.0$$

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

    $$-3+2\times \left|4-6.0\right|=1.0$$

16. Calculate this operation before combining the remaining terms.

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

17. Calculate this operation before combining the remaining terms.

    $$-5+4=-1$$

18. Substitute this x into the inside expression.

    $$1\times \left(-5.0\right)+4=-1.0$$

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

    $$-3+2\times \left|4-5.0\right|=-1.0$$

20. Calculate this operation before combining the remaining terms.

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

21. Calculate this operation before combining the remaining terms.

    $$-4+4=0$$

22. Substitute this x into the inside expression.

    $$1\times \left(-4.0\right)+4=0.0$$

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

    $$-3+2\times \left|4-4.0\right|=-3$$

24. Calculate this operation before combining the remaining terms.

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

25. Calculate this operation before combining the remaining terms.

    $$-3+4=1$$

26. Substitute this x into the inside expression.

    $$1\times \left(-3.0\right)+4=1.0$$

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

    $$-3+2\times \left|4-3.0\right|=-1.0$$

28. Calculate this operation before combining the remaining terms.

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

29. Calculate this operation before combining the remaining terms.

    $$-2+4=2$$

30. Substitute this x into the inside expression.

    $$1\times \left(-2.0\right)+4=2.0$$

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

    $$-3+2\times \left|4-2.0\right|=1.0$$

32. Calculate this operation before combining the remaining terms.

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

33. Calculate this operation before combining the remaining terms.

    $$-1+4=3$$

34. Substitute this x into the inside expression.

    $$1\times \left(-1.0\right)+4=3.0$$

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

    $$-3+2\times \left|4-1.0\right|=3.0$$

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.