Question

graph the equation y = |x| - 5. let x = -3, -2, -1, 0, 1, 2, and 3.
find the y-values for the following points on the graph of the equation.
| x | y
| -3 | □
| -2 | □
| -1 | □
| 0 | □
| 1 | □
| 2 | □
| 3 | □
choose the correct graph of the equation.
○ a. ○ b.
○ c. ○ d.

Explanation:

Step1: Calculate y for x=-3

Substitute \( x = -3 \) into \( y = |x| - 5 \). The absolute value \( |-3| = 3 \), so \( y = 3 - 5 = -2 \).

Step2: Calculate y for x=-2

Substitute \( x = -2 \) into \( y = |x| - 5 \). \( |-2| = 2 \), so \( y = 2 - 5 = -3 \).

Step3: Calculate y for x=-1

Substitute \( x = -1 \) into \( y = |x| - 5 \). \( |-1| = 1 \), so \( y = 1 - 5 = -4 \).

Step4: Calculate y for x=0

Substitute \( x = 0 \) into \( y = |x| - 5 \). \( |0| = 0 \), so \( y = 0 - 5 = -5 \).

Step5: Calculate y for x=1

Substitute \( x = 1 \) into \( y = |x| - 5 \). \( |1| = 1 \), so \( y = 1 - 5 = -4 \).

Step6: Calculate y for x=2

Substitute \( x = 2 \) into \( y = |x| - 5 \). \( |2| = 2 \), so \( y = 2 - 5 = -3 \).

Step7: Calculate y for x=3

Substitute \( x = 3 \) into \( y = |x| - 5 \). \( |3| = 3 \), so \( y = 3 - 5 = -2 \).

For the graph: The equation \( y = |x| - 5 \) is a V - shaped graph (absolute value function) shifted down 5 units. The vertex is at (0, - 5). When x is positive or negative, the graph is symmetric about the y - axis. Looking at the options, option C has a V - shaped graph with vertex at (0, - 5) and passes through the points we calculated (e.g., when x = 1, y=-4; x = 2, y = - 3 etc.). Option A has the vertex at a positive y - value, option B has vertex at a positive y - value, and option D is a linear graph (not absolute value). So the correct graph is C.

Answer:

(for y - values table):

x	y
- 2	- 3
- 1	- 4
0	- 5
1	- 4
2	- 3
3	- 2