Mathematics 10 — Exercise 4.2 · Q1 (i)

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.

   $$x-2=0$$

2. Equate the corresponding entries.

   $$x-2=0$$

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

   $$x=0+2$$

4. Simplify the constant calculation.

   $$x=2$$

5. Divide both sides by the variable coefficient.

   $$x=2\times \frac{1}{1}$$

6. Reduce the fraction.

   $$x=2$$

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

   $$0=0$$

8. Calculate this operation before combining the remaining terms.

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

9. Calculate this operation before combining the remaining terms.

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

10. Calculate this operation before combining the remaining terms.

    $$-1-2=-3$$

11. Substitute this x into the inside expression.

    $$1\times \left(-1.0\right)-2=-3.0$$

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

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

13. Calculate this operation before combining the remaining terms.

    $$1\times 0=0$$

14. Calculate this operation before combining the remaining terms.

    $$0-2=-2$$

15. Substitute this x into the inside expression.

    $$1\times 0.0-2=-2.0$$

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

    $$\left|-2+0.0\right|=2.0$$

17. Calculate this operation before combining the remaining terms.

    $$1\times 1=1$$

18. Calculate this operation before combining the remaining terms.

    $$1-2=-1$$

19. Substitute this x into the inside expression.

    $$1\times 1.0-2=-1.0$$

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

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

21. Calculate this operation before combining the remaining terms.

    $$1\times 2=2$$

22. Calculate this operation before combining the remaining terms.

    $$2-2=0$$

23. Substitute this x into the inside expression.

    $$1\times 2.0-2=0.0$$

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

    $$\left|-2+2.0\right|=0$$

25. Calculate this operation before combining the remaining terms.

    $$1\times 3=3$$

26. Calculate this operation before combining the remaining terms.

    $$3-2=1$$

27. Substitute this x into the inside expression.

    $$1\times 3.0-2=1.0$$

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

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

29. Calculate this operation before combining the remaining terms.

    $$1\times 4=4$$

30. Calculate this operation before combining the remaining terms.

    $$4-2=2$$

31. Substitute this x into the inside expression.

    $$1\times 4.0-2=2.0$$

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

    $$\left|-2+4.0\right|=2.0$$

33. Calculate this operation before combining the remaining terms.

    $$1\times 5=5$$

34. Calculate this operation before combining the remaining terms.

    $$5-2=3$$

35. Substitute this x into the inside expression.

    $$1\times 5.0-2=3.0$$

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

    $$\left|-2+5.0\right|=3.0$$

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

Answer

The final answer is shown below.