We are asked to draw the graph of f(x)=-∣x+3∣−2. To do so, we will use a table of values to find points on the graph. Recall that the absolute value removes the negative sign. In this case, however, we have a negative sign preceding the absolute value. This will take each positive value created by the absolute value and then make it negative, regardless of its original sign.
x | -∣x+3∣−2 | Simplify absolute value | f(x)=-∣x+3∣−2 |
---|---|---|---|
-7 | -∣-7+3∣−2 | -(4)−2 | -6 |
-5 | -∣-5+3∣−2 | -(2)−2 | -4 |
-3 | -∣-3+3∣−2 | -(0)−2 | -2 |
-1 | -∣-1+3∣−2 | -(2)−2 | -4 |
1 | -∣1+3∣−2 | -(4)−2 | -6 |
Now, we will plot and connect the obtained points. Doing that we keep in mind that the graph of an absolute value function has a V
shape.