Mathematics 10 — Exercise 4.2 · Q1 (iii)

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.

   $$x=0$$

2. Equate the corresponding entries.

   $$x=0$$

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

   $$x=0+0$$

4. Simplify the constant calculation.

   $$x=0$$

5. Divide both sides by the variable coefficient.

   $$x=0\times \frac{1}{1}$$

6. Reduce the fraction.

   $$x=0$$

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

   $$0=0$$

8. Calculate this operation before combining the remaining terms.

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

9. Calculate this operation before combining the remaining terms.

   $$-3+0=-3$$

10. Substitute this x into the inside expression.

    $$1\times \left(-3.0\right)+0=-3.0$$

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

    $$5\times \left|-3.0\right|=15.0$$

12. Calculate this operation before combining the remaining terms.

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

13. Calculate this operation before combining the remaining terms.

    $$-2+0=-2$$

14. Substitute this x into the inside expression.

    $$1\times \left(-2.0\right)+0=-2.0$$

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

    $$5\times \left|-2.0\right|=10.0$$

16. Calculate this operation before combining the remaining terms.

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

17. Calculate this operation before combining the remaining terms.

    $$-1+0=-1$$

18. Substitute this x into the inside expression.

    $$1\times \left(-1.0\right)+0=-1.0$$

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

    $$5\times \left|-1.0\right|=5.0$$

20. Calculate this operation before combining the remaining terms.

    $$1\times 0=0$$

21. Calculate this operation before combining the remaining terms.

    $$0+0=0$$

22. Substitute this x into the inside expression.

    $$1\times 0.0+0=0.0$$

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

    $$5\times \left|0.0\right|=0$$

24. Calculate this operation before combining the remaining terms.

    $$1\times 1=1$$

25. Calculate this operation before combining the remaining terms.

    $$1+0=1$$

26. Substitute this x into the inside expression.

    $$1\times 1.0+0=1.0$$

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

    $$5\times \left|1.0\right|=5.0$$

28. Calculate this operation before combining the remaining terms.

    $$1\times 2=2$$

29. Calculate this operation before combining the remaining terms.

    $$2+0=2$$

30. Substitute this x into the inside expression.

    $$1\times 2.0+0=2.0$$

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

    $$5\times \left|2.0\right|=10.0$$

32. Calculate this operation before combining the remaining terms.

    $$1\times 3=3$$

33. Calculate this operation before combining the remaining terms.

    $$3+0=3$$

34. Substitute this x into the inside expression.

    $$1\times 3.0+0=3.0$$

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

    $$5\times \left|3.0\right|=15.0$$

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.