I am doing the piecewise function x+3 if x is less than -2
x^2 if -2 is less than or equal to x which is less than 1, and finally, -x+2 if x is greater than one. The chart says that
x x+3 (x,y)
-3 0 -3,0
-2 1 -2,1
How come the three is negative? Is there a rhyme or reason to this? Thanks!!
The negative sign in front of the three (-3) in the piecewise function is not indicating a negative value. It is simply the value of the function when x is less than -2.
In the given piecewise function, the first condition is that when x is less than -2, the function is defined as x + 3. So when x = -3, we substitute -3 into the equation:
x + 3 = -3 + 3 = 0
Therefore, when x = -3, the value of the function is 0, not -3 as indicated in the chart you provided. Hence, the correct entry should be (-3, 0), not (-3, -3).
For the second entry (-2, 1), when x is exactly equal to -2, we substitute -2 into the equation:
x + 3 = -2 + 3 = 1
Therefore, when x = -2, the value of the function is 1.
In summary, the values in the chart are correct, but the corresponding y-values are slightly mislabeled. The correct values should be (x, y) = (-3, 0) and (-2, 1).